Kalau menghitung luas dan volume suatu bangun ruang itu mah udah biasa ya. Tapi kalo bangun-bangun tersebut digabungkan, luas dan volumenya seperti apa, ya? Yuk, kita pelajari di artikel Matematika kelas 9 ini!
—
Hai gengs, wih kalo udah klik artikel ini, berarti kamu udah selesai belajar konsep masing-masing bangun ruang sisi lengkung, ya?
Inget loh, syarat utama supaya kamu bisa menghitung gabungan luas dan volume bangun ruang sisi lengkung adalah paham konsep masing-masing bangun ruang sisi lengkung itu sendiri.
Bangun ruang sisi lengkung yang udah kita bahas kan ada tabung, kerucut, dan bola. Jadi, untuk paham konsep dari bangun itu semua gak susah kok guys, apalagi rumus luas dan volumenya berkaitan, jadi makin gampang kan buat nempel di otaknya.
Eits, tapi gapapa banget kalo kamu mau baca-baca dulu konsep dari ketiga bangun ruang sisi lengkung ini. Aku setia nungguin kamu kok, tapi jangan lupa balik lagi ya wehehe.
Nah, setelah kamu udah paham betul konsepnya, nih aku kasih bonus tabel rumusnya.
Baca Juga: Cara Menyusun Persamaan Kuadrat dan Contohnya
Rumus-Rumus Bangun Ruang Sisi Lengkung
Konsep Gabungan Bangun Ruang Sisi Lengkung
Sekarang kita fokus ke gabungan bangun ruang sisi lengkung. Coba deh liat dan jawab pertanyaan dari gambar di bawah!
Untuk bagian A, B, dan C, pasti bisa kamu jawab dengan benar. Tapi untuk gambar yang d, pasti ada juga yang bingung, ayo ngaku hehehe!
Well, gambar D itu lah yang disebut gabungan bangun ruang sisi lengkung. Karena dia tersusun dari beberapa bangun ruang sisi lengkung, yaitu tabung tanpa tutup di bagian bawah dan kerucut tanpa atas di bagian atas.
Baca Juga: Apa Bedanya Kongruen dan Sebangun pada Bangun Datar?
Contoh gabungan bangun ruang sisi lengkung di sekitar kita banyak banget loh. Misalnya, tenda sirkus, pensil, obat kapsul, tabung reaksi, pajangan, dan masih banyak lagi.
Pokoknya, buat kamu yang tadi bingung, mulai sekarang gak boleh bingung lagi ya!
Nah, sebelum masuk ke pembahasan soal, ada tips sedikit nih dari aku. Jadi, untuk menghitung luas dan volume gabungan bangun ruang sisi lengkung, kamu wajib bisa menganalisis dan membayangkan bangunnya. Contohnya, bangun tersebut punya tutup/alas atau tidak. Tujuannya, supaya kamu nggak salah ngitung. Oke, kalo gitu kita langsung aja masuk ke soal yang pertama.
Contoh Soal Gabungan Bangun Ruang Sisi Lengkung
Soal 1
Penyelesaian:
Tabung reaksi terbentuk dari gabungan tabung dan setengah bola. Tapi, kamu wajib analisis kedua bangun itu lebih lanjut nih. Tabung tersebut nggak ada tutup alasnya kan, makanya yang kita cari adalah selimut tabungnya. Terus, untuk setengah bola juga nggak ada tutupnya atau disebut dengan bola berongga.
Diketahui:
diameter = 16 mm r = 8 mm
Yang ditanya Luas permukaan, maka rumusnya adalah
Luas permukaan tabung reaksi = luas selimut tabung + luas selimut setengah bola
- Sebelum mencari luas selimut tabung, kita cari dulu tinggi tabung.
Tinggi tabung = tinggi keseluruhan – jari-jari setengah bola
= 150mm – 8mm
= 142 mm
Inget ya guys, karena dalam pilihan ganda (PG) di soal ini tetap, jadi kita nggak perlu ubah ke bentuk bilangan (22/7 atau 3,14).
-
Next, cari luas selimut setengah bola.
Maka, luas permukaan tabung reaksi tersebut adalah :
Oke, kalau cuma bahas 1 soal kurang banget ya?! Kita lanjut ke soal berikutnya.
Soal 2
Penyelesaian:
Cek terlebih dahulu, bahwa tenda tersebut terbentuk dari 2 bangun ruang sisi lengkung, yaitu tabung dan kerucut. Nah, karena pertanyaannya adalah volume, jadi kita bisa langsung menghitung volume tendanya.
Tapi, kalo pertanyaannya adalah luas permukaan, kamu harus analisis lagi bentuk tabung dan kerucutnya, apakah punya tutup dan alas atau tidak.
Diketahui:
Volume tenda = Volume kerucut + volume tabung
Next, kita cari volume tabung!
Jangan lupa cari tinggi tabung terlebih dahulu.
Jadi, volume tenda tersebut adalah
Untuk soal kedua ini, jawaban yang tepat adalah D.
Soal 3
Penyelesaian:
Kalau kamu lihat pensil di atas tersusun dari 3 bangun ruang sisi lengkung, yaitu kerucut, tabung, dan setengah bola. Eits, tapi kita analisis lagi nih, bangun ruang tersebut apakah memiliki tutup/alas?
Jawabannya enggak ya, guys! Ketiga susunan bangun ruangnya terhubung tanpa adanya tutup dan alas. Makanya, kerucut, tabung, dan bola dalam soal ini yang dihitung adalah selimutnya aja. Yuk, kita hitung!
Yang akan kita cari:
Luas permukaan pensil = luas selimut kerucut + luas selimut tabung + luas setengah bola
- Cari luas setengah bola tanpa tutup
Nah, karena kita udah dapat masing-masing nilai luasnya, jadi luas permukaannya adalah
Maka, jawaban yang tepat adalah A.
Soal 4
Sebuah gelas berbentuk tabung memiliki diameter 14 cm dan tinggi 12 cm. Gelas telah terisi teh sebanyak ½ dari total volumenya. Sebongkah batu es berbentuk bola dan berjari-jari 3 cm dimasukkan ke dalam gelas. Berapa tinggi teh dalam gelas setelah batu es dimasukkan ke dalam gelas?
Penyelesaian:
Di soal ini berbeda sama soal sebelumnya ya. Ada 2 bangun ruang yaitu tabung dan bola.
Diketahui:
Yang ditanya adalah tinggi teh dalam gelas setelah batu es dimasukkan.
- Kita cari dulu volume teh dalam gelas
Karena dalam kondisi ini gelas yang berbentuk tabung sudah berisi teh setengah bagian.
Maka, rumusnya menjadi ½ volume tabung, atau bisa ditulis seperti ini:
Next, kita cari volume es batu yang berbentuk bola.
Jadi, tinggi teh di gelas setelah batu es dimasukkan adalah 6,734 cm.
Gimana nih? ternyata seru juga bahas soal gabungan bangun ruang sisi lengkung ini. Hal penting yang harus kamu perhatikan sih bentuk pasti dari bangun yang ada di soal. Jangan sampai salah mengenali struktur bangun ruang sisi lengkungnya ya!
Wah, nggak kerasa nih udah banyak soal yang kita bahas. Tapi, semua soal ini nggak ada artinya kalo kamu nggak lanjut latihan bahas-bahas soal. Supaya kalo dapet soal HOTS, kamu udah santai ngerjainnya.
Ohya, aku juga mau kasih tau nih, kalo ada soal yang belum bisa terpecahkan atau ragu-ragu, langsung aja tanya ke Roboguru. Tinggal foto soalnya, langsung keluar deh jawabannya. Udah gampang, gratis juga loh, mantep kan!
Sampai jumpa di artikel selanjutnya ya, dadah!
Referensi:
Subchan, dkk. (2018) Matematika SMP/MTs Kelas IX. Jakarta : Pusat Perbukuan, Departemen Pendidikan Nasional.
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<h1 class="content-title">
Cara Menghitung Luas & Volume Gabungan Bangun Ruang Sisi Lengkung | Matematika Kelas 9 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/kak-efira-mt-saintek" class="">Kak Efira MT Saintek</a> </p>
<p class="content-info"><span>February 26, 2025 • </span> <span>5 minutes read</span></p>
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<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Header%20Menghitung%20Luas%20Permukaan%20dan%20Volume%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung%20Matematika%20Kelas%209.jpg" alt="Cara Menghitung Luas Permukaan dan Volume Gabungan Bangun Ruang Sisi Lengkung" width="820" /></p>
<blockquote>
<p style="text-align: center;"><em>Kalau menghitung luas dan volume suatu bangun ruang itu mah udah biasa ya. Tapi kalo bangun-bangun tersebut digabungkan, luas dan volumenya seperti apa, ya? Yuk, kita pelajari di <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-9">artikel Matematika kelas 9</a></strong> ini!</em></p>
</blockquote>
<p style="text-align: center;"> —</p>
<p> </p>
<p style="text-align: justify;">Hai gengs, wih kalo udah klik artikel ini, berarti kamu udah selesai belajar konsep masing-masing bangun ruang sisi lengkung, ya?</p>
<p style="text-align: justify;">Inget loh, syarat utama supaya kamu bisa menghitung gabungan luas dan volume bangun ruang sisi lengkung adalah paham konsep masing-masing bangun ruang sisi lengkung itu sendiri.</p>
<p style="text-align: justify;">Bangun ruang sisi lengkung yang udah kita bahas kan ada <strong><a href="/blog/cara-menghitung-volume-dan-luas-permukaan-tabung" rel="noopener">tabung</a></strong>, <strong><a href="https://www.ruangguru.com/blog/rumus-luas-dan-volume-kerucut">kerucut</a></strong>, dan <strong><a href="https://www.ruangguru.com/blog/menghitung-luas-dan-volume-bola">bola</a></strong>. Jadi, untuk paham konsep dari bangun itu semua gak susah kok guys, apalagi rumus luas dan volumenya berkaitan, jadi makin gampang kan buat nempel di otaknya.</p>
<p style="text-align: justify;">Eits, tapi gapapa banget kalo kamu mau baca-baca dulu konsep dari ketiga bangun ruang sisi lengkung ini. Aku setia nungguin kamu kok, tapi jangan lupa balik lagi ya wehehe.</p>
<p style="text-align: justify;">Nah, setelah kamu udah paham betul konsepnya, nih aku kasih bonus tabel rumusnya.</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/blog/menyusun-persamaan-kuadrat" rel="noopener">Cara Menyusun Persamaan Kuadrat dan Contohnya</a></strong></p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Rumus-Rumus Bangun Ruang Sisi Lengkung</span></h2>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rangkuman%20Rumus%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Rangkuman Rumus Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Konsep Gabungan Bangun Ruang Sisi Lengkung</span></h2>
<p style="text-align: justify;">Sekarang kita fokus ke gabungan bangun ruang sisi lengkung. Coba deh liat dan jawab pertanyaan dari gambar di bawah!</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Kuis%20bangun%20ruang%20sisi%20lengkung.jpg" alt="Kuis bangun ruang sisi lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Untuk bagian A, B, dan C, pasti bisa kamu jawab dengan benar. Tapi untuk gambar yang d, pasti ada juga yang bingung, ayo ngaku hehehe!</p>
<p style="text-align: justify;"><em>Well</em>, gambar D itu lah yang disebut gabungan bangun ruang sisi lengkung. Karena dia tersusun dari beberapa bangun ruang sisi lengkung, yaitu tabung tanpa tutup di bagian bawah dan kerucut tanpa atas di bagian atas.</p>
<p style="text-align: justify;"><strong>Baca Juga: <a href="/blog/matematika-kelas-9-apa-bedanya-kongruen-dan-sebangun-pada-bangun-datar" rel="noopener">Apa Bedanya Kongruen dan Sebangun pada Bangun Datar?</a></strong></p>
<p style="text-align: justify;">Contoh gabungan bangun ruang sisi lengkung di sekitar kita banyak banget loh. Misalnya, tenda sirkus, pensil, obat kapsul, tabung reaksi, pajangan, dan masih banyak lagi.</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Contoh%20Benda%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Contoh Benda Gabungan Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Pokoknya, buat kamu yang tadi bingung, mulai sekarang gak boleh bingung lagi ya!</p>
<p style="text-align: justify;">Nah, sebelum masuk ke pembahasan soal, ada tips sedikit nih dari aku. Jadi, untuk menghitung luas dan volume gabungan bangun ruang sisi lengkung, kamu wajib bisa menganalisis dan membayangkan bangunnya. Contohnya, bangun tersebut punya tutup/alas atau tidak. Tujuannya, supaya kamu nggak salah ngitung. Oke, kalo gitu kita langsung aja masuk ke soal yang pertama.</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Contoh Soal Gabungan Bangun Ruang Sisi Lengkung</span></h2>
<p style="text-align: justify;"><span style="font-size: 14pt;"><strong>Soal 1</strong></span></p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Soal%201%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Soal 1 Gabungan Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;"><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;">Tabung reaksi terbentuk dari gabungan tabung dan setengah bola. Tapi, kamu wajib analisis kedua bangun itu lebih lanjut nih. Tabung tersebut nggak ada tutup alasnya kan, makanya yang kita cari adalah selimut tabungnya. Terus, untuk setengah bola juga nggak ada tutupnya atau disebut dengan bola berongga.</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rangka%20Tabung%20Reaksi%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Rangka Tabung Reaksi Gabungan Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Diketahui:</p>
<p style="text-align: justify;">diameter = 16 mm r = 8 mm</p>
<p style="text-align: justify;">Yang ditanya Luas permukaan, maka rumusnya adalah</p>
<p style="text-align: justify;">Luas permukaan tabung reaksi = luas selimut tabung + luas selimut setengah bola</p>
<ul style="text-align: justify;">
<li aria-level="1">Sebelum mencari luas selimut tabung, kita cari dulu tinggi tabung.<br />
Tinggi tabung = tinggi keseluruhan – jari-jari setengah bola<br />
= 150mm – 8mm<br />
= 142 mm</li>
</ul>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-10-45-13-AM.png" width="600" /></p>
<p style="text-align: justify;">Inget ya guys, karena dalam pilihan ganda (PG) <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-12-24-57-AM.png" width="14" /> di soal ini tetap, jadi kita nggak perlu ubah ke bentuk bilangan (22/7 atau 3,14).</p>
<p> </p>
<ul style="text-align: justify;">
<li aria-level="1"><em>Next</em>, cari luas selimut setengah bola.</li>
</ul>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-13-19-72-AM.png" /></p>
<p style="text-align: justify;">Maka, luas permukaan tabung reaksi tersebut adalah :</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-14-40-11-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Oke, kalau cuma bahas 1 soal kurang banget ya?! Kita lanjut ke soal berikutnya.</p>
<p> </p>
<p style="text-align: justify;"><span style="font-size: 14pt;"><strong>Soal 2</strong></span></p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Soal%202%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung%20-%20Matematika.jpg" alt="Soal 2 Gabungan Bangun Ruang Sisi Lengkung - Matematika" width="600" /></p>
<p> </p>
<p style="text-align: justify;"><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;">Cek terlebih dahulu, bahwa tenda tersebut terbentuk dari 2 bangun ruang sisi lengkung, yaitu tabung dan kerucut. Nah, karena pertanyaannya adalah volume, jadi kita bisa langsung menghitung volume tendanya.</p>
<p style="text-align: justify;">Tapi, kalo pertanyaannya adalah luas permukaan, kamu harus analisis lagi bentuk tabung dan kerucutnya, apakah punya tutup dan alas atau tidak.</p>
<p style="text-align: justify;">Diketahui:</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-17-08-31-AM.png" /></p>
<p style="text-align: justify;">Volume tenda = Volume kerucut + volume tabung</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Menghitung%20tinggi%20kerucut%20dari%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Menghitung tinggi kerucut dari Gabungan Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-18-55-95-AM.png" /></p>
<p style="text-align: justify;"><em>Next</em>, kita cari volume tabung!</p>
<p style="text-align: justify;">Jangan lupa cari tinggi tabung terlebih dahulu.<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-19-52-53-AM.png" /></p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-21-02-35-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Jadi, volume tenda tersebut adalah</p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-21-37-58-AM.png" /><br />
<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-22-46-45-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Untuk soal kedua ini, jawaban yang tepat adalah D.</p>
<p> </p>
<p style="text-align: justify;"><span style="font-size: 14pt;"><strong>Soal 3</strong></span></p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Soal%203%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Soal 3 Gabungan Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;"><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;">Kalau kamu lihat pensil di atas tersusun dari 3 bangun ruang sisi lengkung, yaitu kerucut, tabung, dan setengah bola. Eits, tapi kita analisis lagi nih, bangun ruang tersebut apakah memiliki tutup/alas?</p>
<p style="text-align: justify;">Jawabannya enggak ya, guys! Ketiga susunan bangun ruangnya terhubung tanpa adanya tutup dan alas. Makanya, kerucut, tabung, dan bola dalam soal ini yang dihitung adalah selimutnya aja. Yuk, kita hitung!</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-24-35-47-AM.png" /></p>
<p style="text-align: justify;">Yang akan kita cari:</p>
<p style="text-align: justify;">Luas permukaan pensil = luas selimut kerucut + luas selimut tabung + luas setengah bola</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Mencari%20garis%20pelukis%20atau%20sisi%20miring%20dari%20kerucut-%20Bangun%20Ruang%20Sisi%20Lengkung.jpg" alt="Mencari garis pelukis atau sisi miring dari kerucut- Bangun Ruang Sisi Lengkung" width="600" /></p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-26-08-85-AM.png" /></p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Menghitung%20Luas%20Permukaan%20dan%20Volume%20Gabungan%20Bangun%20Ruang%20Sisi%20Lengkung%20-%20Matematika%20Kelas%209-12%20(1).jpg" alt="Menghitung Luas Permukaan dan Volume Gabungan Bangun Ruang Sisi Lengkung - Matematika Kelas 9-12 (1)" width="600" /></p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-16-2022-04-28-10-95-AM.png" /></p>
<p> </p>
<ul style="text-align: justify;">
<li aria-level="1">Cari luas setengah bola tanpa tutup</li>
</ul>
<p> </p>
<p><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-27-47-53-AM.png" /></p>
<p> </p>
<p>Nah, karena kita udah dapat masing-masing nilai luasnya, jadi luas permukaannya adalah <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Feb-16-2022-04-29-40-58-AM.png" /></p>
<p style="text-align: justify;">Maka, jawaban yang tepat adalah A.</p>
<p> </p>
<p style="text-align: justify;"><span style="font-size: 14pt;"><strong>Soal 4</strong></span></p>
<p style="text-align: justify;">Sebuah gelas berbentuk tabung memiliki diameter 14 cm dan tinggi 12 cm. Gelas telah terisi teh sebanyak ½ dari total volumenya. Sebongkah batu es berbentuk bola dan berjari-jari 3 cm dimasukkan ke dalam gelas. Berapa tinggi teh dalam gelas setelah batu es dimasukkan ke dalam gelas?</p>
<p style="text-align: justify;"><strong>Penyelesaian:</strong></p>
<p style="text-align: justify;">Di soal ini berbeda sama soal sebelumnya ya. Ada 2 bangun ruang yaitu tabung dan bola.</p>
<p style="text-align: justify;">Diketahui:</p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-40-15-31-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Yang ditanya adalah tinggi teh dalam gelas setelah batu es dimasukkan.</p>
<p> </p>
<ul style="text-align: justify;">
<li aria-level="1">Kita cari dulu volume teh dalam gelas</li>
</ul>
<p style="text-align: justify;">Karena dalam kondisi ini gelas yang berbentuk tabung sudah berisi teh setengah bagian.</p>
<p style="text-align: justify;">Maka, rumusnya menjadi ½ volume tabung, atau bisa ditulis seperti ini:</p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-30-47-14-AM.png" /></p>
<p> </p>
<p style="text-align: justify;"><em>Next</em>, kita cari volume es batu yang berbentuk bola.</p>
<p> </p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-31-14-89-AM.png" /></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Jan-13-2022-03-31-50-56-AM.png" /></p>
<p> </p>
<p style="text-align: justify;">Jadi, tinggi teh di gelas setelah batu es dimasukkan adalah 6,734 cm.</p>
<p style="text-align: justify;">Gimana nih? ternyata seru juga bahas soal gabungan bangun ruang sisi lengkung ini. Hal penting yang harus kamu perhatikan sih bentuk pasti dari bangun yang ada di soal. Jangan sampai salah mengenali struktur bangun ruang sisi lengkungnya ya!</p>
<p style="text-align: justify;">Wah, nggak kerasa nih udah banyak soal yang kita bahas. Tapi, semua soal ini nggak ada artinya kalo kamu nggak lanjut latihan bahas-bahas soal. Supaya kalo dapet soal HOTS, kamu udah santai ngerjainnya.</p>
<p style="text-align: justify;">Ohya, aku juga mau kasih tau nih, kalo ada soal yang belum bisa terpecahkan atau ragu-ragu, langsung aja tanya ke <a href="https://api.whatsapp.com/send/?phone=6281578150000&text=ROBOGURU&app_absent=0&__hstc=215722120.859ba186793861d6c87477708adc70c3.1629746889303.1640634930843.1640641825756.61&__hssc=215722120.1.1640711823437&__hsfp=1461018766&hsCtaTracking=19d4813c-1d17-40c2-aafd-8717bd39cd86%7C7a8ca196-dc7c-414b-8405-f26bcab6a94e" target="_blank" rel="noopener"><strong>Roboguru</strong></a>. Tinggal foto soalnya, langsung keluar deh jawabannya. Udah gampang, gratis juga loh, mantep kan!</p>
<p style="text-align: justify;">Sampai jumpa di artikel selanjutnya ya, dadah!</p>
<p style="text-align: justify;"><a href="https://roboguru.ruangguru.com/" target="_blank" rel="noopener"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/cta/a80c2f9d-5f1a-424f-b9cf-6b4c6f362d2a.jpeg" alt="Roboguru Whatsapp" /></a></p>
<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: left;">Subchan, dkk. (2018) Matematika SMP/MTs Kelas IX. Jakarta : Pusat Perbukuan, Departemen Pendidikan Nasional.</p>
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<li><a href="https://www.ruangguru.com/beasiswa">Beasiswa Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/cicilan">Cicilan Ruangguru</a></li>
<li><a href="https://www.ruangguru.com/promo">Promo Ruangguru</a></li>
<li><a href="https://ticketing.ruangguru.com/help?request_type_id=459" target="_blank">Vulnerability Report</a></li>
<li><a href="https://www.ruangguru.com/bantuan#layanan">Layanan Pengaduan</a></li>
<li><a href="https://www.ruangguru.com/terms-conditions">Syarat & Ketentuan</a></li>
<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
<ul type="none">
<li><a href="https://www.brainacademy.id/" target="_blank">Brain Academy</a></li>
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<li><a href="https://skillacademy.com/" target="_blank">Skill Academy</a></li>
<li><a href="https://www.ruangkerja.id/" target="_blank">Ruangkerja</a></li>
<li><a href="https://www.schoters.com/id/" target="_blank">Schoters</a></li>
<li><a href="https://www.kalananti.id/" target="_blank">Kalananti</a></li>
</ul>
</nav>
</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
<a target="_blank" rel="nofollow" href="https://apps.apple.com/id/app/ruangguru-solusi-belajar/id1099742206?l=id">
<img src="https://cdn-web-2.ruangguru.com/static/appstore.png" loading="lazy" alt="Button App Store Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://play.google.com/store/apps/details?id=com.ruangguru.livestudents&hl=in">
<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
</li>
<li>
<a target="_blank" rel="nofollow" href="https://appgallery.huawei.com/#/app/C102352375">
<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
</li>
</ul>
</div>
</nav>
</div>
</div>
</div>
</div>
<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
<a target="_blank" href="https://www.instagram.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/instagram.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.facebook.com/ruanggurucom/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/facebook.png" loading="lazy" alt="Logo Facebook Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://twitter.com/ruangguru/">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/twitter.png" loading=" lazy" alt="Logo Twitter Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.youtube.com/ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/youtube.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/youtube.png" loading=" lazy" alt="Logo Youtube Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.linkedin.com/company/ruangguru-com">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60&convert=webp" type="image/webp">
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<img src="https://cdn-web-2.ruangguru.com/static/linkedin.png" loading=" lazy" alt="Logo LinkedIn Footer" width="32px" height="32px" />
</picture>
</a>
<a target="_blank" href="https://www.tiktok.com/@ruangguru">
<picture>
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60&convert=webp" type="image/webp">
<source srcset="https://cdn-web-2.ruangguru.com/static/tiktok.png?height=60" type="image/png">
<img src="https://cdn-web-2.ruangguru.com/static/tiktok.png" loading=" lazy" alt="Logo TikTok Footer" width="32px" height="32px" />
</picture>
</a>
</nav>
</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>