Yuk, kita belajar cara menghitung luas dan volume bola lewat artikel Matematika kelas 9 ini. Ada contoh soalnya juga, lho!
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Guys, kalian tau nggak, ternyata menurut skala survei Indonesia, ada 90,8% masyarakat Indonesia yang mengetahui olahraga sepak bola. Nggak cuma itu aja, sebanyak 47,6% menyukainya. Persentase ini mengalahkan olahraga lainnya, seperti bulutangkis dengan persentase 18,8%.
Hmmm… nggak heran sih ya, terbukti dari banyaknya anak-anak kecil yang mengidolakan tokoh pemain bola, kayak Cristiano Ronaldo. Bahkan, orang dewasa pun sering begadang untuk nungguin klub kesayangannya tanding. Oh ya, nggak cuma laki-laki aja loh yang menyukai olahraga ini, banyak juga perempuan yang senang dengan sepak bola.
Tapi, kamu pernah kepikiran nggak sih, kalo bola sepak menggunakan bola dengan bentuk lain? Seperti misalnya bola rugby, kan bisa menggelinding juga tuh, coba deh bayangin!
Bola Rugby (Sumber Gambar: unsplash.com)
Hahaha, iya sih bisa menggelinding, tapi pasti bakalan susah banget. Udah gitu, pemain sepak bola akan susah ketika mengoper ke temannya.
Nah, dari sini kita bisa tau ya, bola sepak bisa menggelinding dengan baik, dan pemain pun bisa dengan mudah menggiring, mengoper, dan menendang bola ke gawang. Rahasianya adalah karena bola sepak termasuk bangun ruang sisi lengkung.
Apa itu Bangun Ruang Bola?
Bola adalah bangun ruang sisi lengkung yang dibentuk dari setengah lingkaran yang diputar mengelilingi garis tengahnya.
Kerangka Bola (sumbe Youtube: Omega Open Course)
Sifat-Sifat Bangun Ruang Bola
Untuk bisa lebih mengenal bola, kita harus tau sifat-sifatnya. Kamu bisa ingat sifat-sifat bola ini ya:
- Memiliki satu titik pusat.
- Tidak memiliki titik sudut.
- Tidak memiliki rusuk.
- Tidak memiliki diagonal bidang dan diagonal ruang.
- Memiliki satu sisi yang disebut dinding bola.
- Memiliki jari-jari (r), yaitu jarak titik pusat ke dinding bola.
- Terdapat diameter (d), yaitu jarak dinding ke dinding melewati titik pusat.
Jenis-Jenis Bangun Ruang Bola
Btw, kamu tau nggak kalo bola itu terbagi jadi 2 macam? yaitu bola pejal dan bola berongga. Apa sih bedanya?
Bola pejal adalah bola padat, yang volumenya selalu berisi. Contoh gampangnya tuh kayak bakso. Semantara itu, bola berongga adalah bola biasa yang dalamnya tidak berisi. Contohnya tuh, bisa tahu bulat wkwkwk, atau bola plastik mainan bayi, dan masih banyak lagi.
Setelah kamu tau sifat, dan macam-macam bola, sekarang cari tahu rumus dari luas dan volume bola, yuk!
Rumus Volume Bola dan Contoh Soal
Sebenarnya sama aja sih kayak bangun ruang lainnya, bola punya luas dan volumenya sendiri. Tapi, sebelum ke volume bola, kamu udah harus paham volume kerucut ya, karena keduanya berhubungan.
Baca Juga: Cara Menghitung Luas dan Volume Kerucut
Ilustrasinya gini, misal kita isi kerucut penuh dengan air, setelah itu air dari kerucut kita pindahkan ke bola. Ternyata, dibutuhkan 2 kerucut penuh air untuk mengisi semua ruang bola. Supaya kamu lebih kebayang, kamu bisa perhatikan video di bawah ini dulu ya!
(Sumber Youtube: Kyle Pearce)
Lewat video di atas, kita bisa nemuin rumus volume bola. Tapi, ada yang harus di-highlight nih guys, tinggi kerucut itu 2 kali jari-jari bola, ya. Jadi, dengan jari-jari yang sama antar kedua bangun (kerucut dan bola), maka volume bola adalah 2 × volume kerucut.
Bisa ditulis, jadi kaya gini ya guys:
Nah, supaya makin paham, langsung masuk ke contoh soal ya.
Terdapat benda pejal berbentuk seperempat bola dengan diameter 20 cm. Volume benda tersebut adalah …
Pembahasan:
Diameter bola = 20 cm, r = 10 cm.
Bentuk seperempat bola pejal, maka rumusnya seperti ini,
Maka jawaban yang tepat adalah B. 1046,66.
Gimana, gampang, kan?
Next, kita bahas rumus luas permukaan bola, yuk!
Rumus Luas Permukaan Bola dan Contoh Soal
Kalo tadi volume bola sama dengan 2 × volume kerucut, nah kalo luas permukaan bola bisa dihitung lewat luas persegi panjang. Persegi panjang itu kan punya 2 sisi, yaitu panjang dan lebar.
Nah, sisi panjangnya sama dengan keliling lingkaran, terus untuk lebarnya sama dengan 2 jari-jarinya.
Ilustrasi Luas Permukaan Bola (Sumber Youtube: 3Blue1Brown)
Sesuai ilustrasi di atas, bisa disusun rumusnya ya. Ini dia rumus luas permukaan bola. Kamu wajib ingat!
Oke, sekarang kalo seandainya ada bola terus kita potong dengan bagian yang sama, menurut kamu luas permukaannya masih sama nggak? Enggak ya guys. Rumus luas setengah permukaan bola tinggal kita kalikan setengah aja. Jadi gini ya guys!
Tapi, khusus untuk rumus luas permukaan setengah bola pejal beda lagi ya. Loh kok gitu? itu karena bola pejal berisi. Kamu bayangin aja ketika kamu memotong semangka jadi 2 bagian yang sama besar. Kamu bakal nemuin permukaan yang berbentuk lingkaran. Jadi luas permukaan setengah bola tadi ditambah luas lingkaran. Penulisannya, kayak gini:
Rumus-rumus itu bisa kita aplikasikan di contoh soal ini ya, guys!
Jika luas permukaan bola adalah 1.808,64 berapakah diameter bola tersebut?
Pembahasan:
Diketahui luas permukaan bola adalah 1.808,64
Karena yang ditanya adalah diameter, dimana diameter adalah 2 × jari-jari, sehingga 2 × 12= 24 cm.
Baca Juga: Rumus Volume Tabung, Luas Permukaan & Keliling Alas
Lewat beberapa rumus yang udah kita pelajarin, jangan kebalik dan bingung ya guys. Oh ya, ada sedikit tips nih, waktu kamu lagi baca soal tentang bola, sebisa mungkin sambil kamu bayangkan ya. Karena, dari situlah kamu bisa menggunakan rumus yang tepat dan nggak kebingungan walaupun soal yang dikasih bervariasi.
Bonus tips buat kamu! Inget ya jangan berhenti sampai disini aja. Kamu harus banget latihan soal-soal di ruangbelajar. Semua soalnya diupdate terus menerus, dan kamu bisa langsung dapat pembahasannya, ditambah ada pembahasan konsep langsung dari master teacher ruangguru yang asik banget. Yuk, tunggu apalagi, langganan sekarang ya, dadah!
Referensi:
Subchan, Winarni, Hanafi L, dkk. (2015) Matematika SMP/MTs Kelas IX Semester 1. Jakarta: Kementerian Pendidikan dan Kebudayaan
Sumber Gambar dan Video:
“But why is a sphere’s surface area four times its shadow?”. [Daring] Tautan: https://www.youtube.com/watch?v=GNcFjFmqEc8&t=616s (diakses pada tanggal 26 Oktober 2021)
Spherical Coordinate System. [Daring] Tautan: https://www.youtube.com/watch?v=FDyenWWlPdU&t=160s (diakses pada tanggal 25 Oktober 2021)
Visualizing the volume of a Sphere Formula. [Daring]. Tautan: https://www.youtube.com/watch?v=YNutS8eIhEs (diakses pada tanggal 25 Oktober 2021)
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<h1 class="content-title">
Rumus Luas dan Volume Bola, Cara Menghitung, serta Contohnya | 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>July 1, 2025 • </span> <span>5 minutes read</span></p>
<br />
</div>
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<p style="line-height: 1.5;"><img decoding="async" style="width: 820px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Cara%20Menghitung%20Luas%20dan%20Volume%20Bola.jpg" alt="Cara Menghitung Luas dan Volume Bola" /></p>
<blockquote>
<p style="line-height: 1.5; text-align: center; font-size: 16px;"><em>Yuk, kita belajar cara menghitung luas dan volume bola lewat <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-9">artikel Matematika kelas 9</a></strong> ini. Ada contoh soalnya juga, lho!</em></p>
</blockquote>
<p style="line-height: 1.5; text-align: center;">—</p>
<p> </p>
<p style="line-height: 1.5; text-align: justify;">Guys, kalian tau nggak, ternyata menurut skala survei Indonesia, ada 90,8% masyarakat Indonesia yang mengetahui olahraga sepak bola. Nggak cuma itu aja, sebanyak 47,6% menyukainya. Persentase ini mengalahkan <span style="font-weight: bold;">olahraga lainnya</span>, seperti bulutangkis dengan persentase 18,8%.</p>
<p style="text-align: justify;">Hmmm… nggak heran sih ya, terbukti dari banyaknya anak-anak kecil yang mengidolakan tokoh pemain bola, kayak Cristiano Ronaldo. Bahkan, orang dewasa pun sering begadang untuk nungguin klub kesayangannya tanding. Oh ya, nggak cuma laki-laki aja loh yang menyukai olahraga ini, banyak juga perempuan yang senang dengan sepak bola.</p>
<p style="text-align: justify;">Tapi, kamu pernah kepikiran nggak sih, kalo bola sepak menggunakan bola dengan bentuk lain? Seperti misalnya bola rugby, kan bisa menggelinding juga tuh, coba deh bayangin!</p>
<p style="text-align: center;"><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img fetchpriority="high" decoding="async" style="height: auto; max-width: 100%; width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/marcos-ramirez-zGxlVXGg2Tg-unsplash.jpg" alt="bola rugby" width="600" height="397" /></span></p>
<p style="text-align: center;">Bola Rugby (Sumber Gambar: unsplash.com)</p>
<p> </p>
<p style="text-align: justify;">Hahaha, iya sih bisa menggelinding, tapi pasti bakalan susah banget. Udah gitu, pemain sepak bola akan susah ketika mengoper ke temannya.</p>
<p style="text-align: justify;">Nah, dari sini kita bisa tau ya, bola sepak bisa menggelinding dengan baik, dan pemain pun bisa dengan mudah menggiring, mengoper, dan menendang bola ke gawang. Rahasianya adalah karena bola sepak termasuk bangun ruang sisi lengkung.</p>
<p> </p>
<h2><span style="font-size: 18pt;">Apa itu Bangun Ruang Bola?</span></h2>
<p style="text-align: justify; font-weight: bold;">Bola adalah bangun ruang sisi lengkung yang dibentuk dari setengah lingkaran yang diputar mengelilingi garis tengahnya.</p>
<div class="hs-embed-wrapper" style="position: relative; overflow: hidden; width: 100%; height: auto; padding: 0px; max-width: 600px; min-width: 256px; display: block; margin: auto;" data-service="youtube" data-responsive="true">
<div class="hs-embed-content-wrapper">
<div style="position: relative; overflow: hidden; max-width: 100%; padding-bottom: 56.5%; margin: 0px;"><iframe style="position: absolute; top: 0px; left: 0px; width: 100%; height: 100%; border: none;" title="Spherical Coordinate System (With 3D Animation)" src="https://www.youtube.com/embed/FDyenWWlPdU?feature=oembed" width="200" height="113" frameborder="0" allowfullscreen="allowfullscreen"></iframe></div>
</div>
</div>
<p style="text-align: center;">Kerangka Bola (sumbe Youtube: Omega Open Course)</p>
<p> </p>
<h2><span style="font-size: 18pt;">Sifat-Sifat Bangun Ruang Bola</span></h2>
<p style="text-align: justify;">Untuk bisa lebih mengenal bola, kita harus tau sifat-sifatnya. Kamu bisa ingat sifat-sifat bola ini ya:</p>
<ol>
<li style="text-align: justify;" aria-level="1">Memiliki satu titik pusat.</li>
<li style="text-align: justify;" aria-level="1">Tidak memiliki titik sudut.</li>
<li style="text-align: justify;" aria-level="1">Tidak memiliki rusuk.</li>
<li style="text-align: justify;" aria-level="1">Tidak memiliki diagonal bidang dan diagonal ruang.</li>
<li style="text-align: justify;" aria-level="1">Memiliki satu sisi yang disebut dinding bola.</li>
<li style="text-align: justify;" aria-level="1">Memiliki jari-jari (r), yaitu jarak titik pusat ke dinding bola.</li>
<li style="text-align: justify;" aria-level="1">Terdapat diameter (d), yaitu jarak dinding ke dinding melewati titik pusat.</li>
</ol>
<p> </p>
<h2><span style="font-size: 18pt;">Jenis-Jenis Bangun Ruang Bola</span></h2>
<p style="text-align: justify;">Btw, kamu tau nggak kalo bola itu terbagi jadi 2 macam? yaitu bola pejal dan bola berongga. Apa sih bedanya?</p>
<p style="text-align: justify;"><span style="font-weight: bold;">Bola pejal adalah bola padat, yang volumenya selalu berisi</span>. Contoh gampangnya tuh kayak bakso. Semantara itu, <span style="font-weight: bold;">bola berongga adalah bola biasa yang dalamnya tidak berisi</span>. Contohnya tuh, bisa tahu bulat wkwkwk, atau bola plastik mainan bayi, dan masih banyak lagi.</p>
<p style="text-align: justify;">Setelah kamu tau sifat, dan macam-macam bola, sekarang cari tahu rumus dari luas dan volume bola, yuk!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Rumus Volume Bola dan Contoh Soal</span></h2>
<p style="text-align: justify;">Sebenarnya sama aja sih kayak bangun ruang lainnya, bola punya luas dan volumenya sendiri. Tapi, sebelum ke volume bola, kamu udah harus paham volume kerucut ya, karena keduanya berhubungan.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/rumus-luas-dan-volume-kerucut">Cara Menghitung Luas dan Volume Kerucut</a></strong></p>
<p style="text-align: justify;">Ilustrasinya gini, misal kita isi kerucut penuh dengan air, setelah itu air dari kerucut kita pindahkan ke bola. Ternyata, dibutuhkan 2 kerucut penuh air untuk mengisi semua ruang bola. Supaya kamu lebih kebayang, kamu bisa perhatikan video di bawah ini dulu ya!</p>
<div class="hs-embed-wrapper" style="position: relative; overflow: hidden; width: 100%; height: auto; padding: 0px; max-width: 600px; min-width: 256px; display: block; margin: auto;" data-service="youtube" data-responsive="true">
<div class="hs-embed-content-wrapper">
<div style="position: relative; overflow: hidden; max-width: 100%; padding-bottom: 56.5%; margin: 0px;"><iframe style="position: absolute; top: 0px; left: 0px; width: 100%; height: 100%; border: none;" title="Cones and Spheres [ACT 3]: How Many Cones Does It Take To Fill a Sphere?" src="https://www.youtube.com/embed/PaA-g_z_E2E?feature=oembed" width="200" height="113" frameborder="0" allowfullscreen="allowfullscreen"></iframe></div>
</div>
</div>
<p style="text-align: center;">(Sumber Youtube: Kyle Pearce)</p>
<p> </p>
<p style="text-align: justify;">Lewat video di atas, kita bisa nemuin rumus volume bola. Tapi, ada yang harus di-<em>highlight</em> nih guys, tinggi kerucut itu 2 kali jari-jari bola, ya. Jadi, dengan jari-jari yang sama antar kedua bangun (kerucut dan bola), maka volume bola adalah 2 × volume kerucut.</p>
<p>Bisa ditulis, jadi kaya gini ya guys:</p>
<p><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rumus%20Volume%20Bola.jpg" alt="Rumus Volume Bola" width="600" /></span></p>
<p> </p>
<p>Nah, supaya makin paham, langsung masuk ke contoh soal ya.</p>
<p>Terdapat benda pejal berbentuk seperempat bola dengan diameter 20 cm. Volume benda tersebut adalah …<span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-07-32-58-PM.png" /></span></p>
<p><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-08-07-62-PM.png" /></span></p>
<p> </p>
<p> </p>
<p style="font-weight: bold;">Pembahasan:</p>
<p>Diameter bola = 20 cm, r = 10 cm.</p>
<p>Bentuk seperempat bola pejal, maka rumusnya seperti ini,</p>
<p style="text-align: justify;"><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-10-12-09-PM.png" /></span></p>
<p>Maka jawaban yang tepat adalah B. 1046,66.</p>
<p>Gimana, gampang, kan?</p>
<p style="text-align: justify; font-size: 16px;">Next, kita bahas rumus luas permukaan bola, yuk!</p>
<p> </p>
<h2><span style="font-size: 18pt;">Rumus Luas Permukaan Bola dan Contoh Soal</span></h2>
<p style="text-align: justify;">Kalo tadi volume bola sama dengan 2 × volume kerucut, nah kalo luas permukaan bola bisa dihitung lewat luas persegi panjang. Persegi panjang itu kan punya 2 sisi, yaitu panjang dan lebar.</p>
<p style="text-align: justify;">Nah, sisi panjangnya sama dengan keliling lingkaran, terus untuk lebarnya sama dengan 2 jari-jarinya.</p>
<div class="hs-embed-wrapper" style="position: relative; overflow: hidden; width: 100%; height: auto; padding: 0px; max-width: 600px; min-width: 256px; display: block; margin: auto;" data-service="youtube" data-responsive="true">
<div class="hs-embed-content-wrapper">
<div style="position: relative; overflow: hidden; max-width: 100%; padding-bottom: 56.5%; margin: 0px;"><iframe loading="lazy" style="position: absolute; top: 0px; left: 0px; width: 100%; height: 100%; border: none;" title="But why is a sphere's surface area four times its shadow?" src="https://www.youtube.com/embed/GNcFjFmqEc8?feature=oembed" width="200" height="113" frameborder="0" allowfullscreen="allowfullscreen"></iframe></div>
</div>
</div>
<p style="text-align: center;">Ilustrasi Luas Permukaan Bola (Sumber Youtube: 3Blue1Brown)</p>
<p> </p>
<p>Sesuai ilustrasi di atas, bisa disusun rumusnya ya. Ini dia rumus luas permukaan bola. Kamu wajib ingat!</p>
<p><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rumus%20Luas%20Permukaan%20Bola.jpg" alt="Rumus Luas Permukaan Bola" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Oke, sekarang kalo seandainya ada bola terus kita potong dengan bagian yang sama, menurut kamu luas permukaannya masih sama nggak? Enggak ya guys. Rumus luas setengah permukaan bola tinggal kita kalikan setengah aja. Jadi gini ya guys!</p>
<p><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rumus%20Luas%20Permukaan%20Setengah%20Bola.jpg" alt="Rumus Luas Permukaan Setengah Bola" width="600" /></span></p>
<p> </p>
<p style="text-align: justify;">Tapi, khusus untuk rumus luas permukaan setengah bola pejal beda lagi ya. Loh kok gitu? itu karena bola pejal berisi. Kamu bayangin aja ketika kamu memotong semangka jadi 2 bagian yang sama besar. Kamu bakal nemuin permukaan yang berbentuk lingkaran. Jadi luas permukaan setengah bola tadi ditambah luas lingkaran. Penulisannya, kayak gini:</p>
<p style="text-align: justify;"><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" style="width: 600px; margin-left: auto; margin-right: auto; display: block;" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/Rumus%20Luas%20Permukaan%20Setengah%20Bola%20Pejal.jpg" alt="Rumus Luas Permukaan Setengah Bola Pejal" width="600" /></span></p>
<p> </p>
<p>Rumus-rumus itu bisa kita aplikasikan di contoh soal ini ya, guys!</p>
<p style="text-align: justify;">Jika luas permukaan bola adalah 1.808,64 <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-14-59-05-PM.png" /> berapakah diameter bola tersebut? <img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-15-22-52-PM.png" /></p>
<p style="text-align: justify;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-15-37-57-PM.png" /></p>
<p> </p>
<p> </p>
<p style="font-weight: bold;">Pembahasan:</p>
<p>Diketahui luas permukaan bola adalah 1.808,64<img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-17-16-89-PM.png" /></p>
<p style="text-align: justify;"><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><img decoding="async" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/image-png-Nov-04-2021-12-17-40-53-PM.png" /></span></p>
<p> </p>
<p style="text-align: justify;">Karena yang ditanya adalah diameter, dimana diameter adalah 2 × jari-jari, sehingga 2 × 12= 24 cm.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/cara-menghitung-volume-dan-luas-permukaan-tabung">Rumus Volume Tabung, Luas Permukaan & Keliling Alas</a></strong></p>
<p style="text-align: justify;">Lewat beberapa rumus yang udah kita pelajarin, jangan kebalik dan bingung ya guys. Oh ya, ada sedikit tips nih, waktu kamu lagi baca soal tentang bola, sebisa mungkin sambil kamu bayangkan ya. Karena, dari situlah kamu bisa menggunakan rumus yang tepat dan nggak kebingungan walaupun soal yang dikasih bervariasi.</p>
<p style="text-align: justify;">Bonus tips buat kamu! Inget ya jangan berhenti sampai disini aja. Kamu harus banget latihan soal-soal di <strong><a href="https://www.ruangguru.com/ruangbelajar" target="_blank" rel="noopener">ruangbelajar</a></strong>. Semua soalnya diupdate terus menerus, dan kamu bisa langsung dapat pembahasannya, ditambah ada pembahasan konsep langsung dari master teacher ruangguru yang asik banget. Yuk, tunggu apalagi, langganan sekarang ya, dadah!</p>
<p><span style="font-family: Georgia, Palatino, Times, 'Times New Roman', serif;"><a href="https://app.ruangguru.com/ruangbelajar/"><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/a2dbab8e-e903-4b70-ae04-39ff5807647e.jpg" alt="CTA ruangbelajar" width="820" /></a></span></p>
<p style="font-weight: bold;">Referensi:</p>
<p style="text-align: left;">Subchan, Winarni, Hanafi L, dkk. (2015) Matematika SMP/MTs Kelas IX Semester 1. Jakarta: Kementerian Pendidikan dan Kebudayaan</p>
<p style="font-weight: bold; text-align: left;">Sumber Gambar dan Video:</p>
<p style="text-align: left;">“But why is a sphere’s surface area four times its shadow?”. [Daring] Tautan: https://www.youtube.com/watch?v=GNcFjFmqEc8&t=616s (diakses pada tanggal 26 Oktober 2021)</p>
<p style="text-align: left;">Spherical Coordinate System. [Daring] Tautan: https://www.youtube.com/watch?v=FDyenWWlPdU&t=160s (diakses pada tanggal 25 Oktober 2021)</p>
<p style="text-align: left;">Visualizing the volume of a Sphere Formula. [Daring]. Tautan: https://www.youtube.com/watch?v=YNutS8eIhEs (diakses pada tanggal 25 Oktober 2021)</p>
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<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">
<source srcset="https://cdn-web-2.ruangguru.com/static/facebook.png?height=60" type="image/png">
<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">
<source srcset="https://cdn-web-2.ruangguru.com/static/twitter.png?height=60" type="image/png">
<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">
<source srcset="https://cdn-web-2.ruangguru.com/static/linkedin.png?height=60" type="image/png">
<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">
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<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>