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2026-01-01
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<p>228 Learners</p>
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<p>Last updated on<strong>August 10, 2025</strong></p>
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<p>Last updated on<strong>August 10, 2025</strong></p>
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<p>In 3D geometry, we explore various formulas related to solids, their volumes, surface areas, and coordinates in three-dimensional space. This topic covers the essential formulas needed for understanding 3D geometry in mathematics.</p>
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<p>In 3D geometry, we explore various formulas related to solids, their volumes, surface areas, and coordinates in three-dimensional space. This topic covers the essential formulas needed for understanding 3D geometry in mathematics.</p>
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<h2>List of 3D Geometry Formulas</h2>
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<h2>List of 3D Geometry Formulas</h2>
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<p>In 3D<a>geometry</a>, key<a>formulas</a>include those for calculating volumes, surface areas, and coordinates<a>of</a>points in space. Let’s learn these essential formulas for 3D geometry.</p>
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<p>In 3D<a>geometry</a>, key<a>formulas</a>include those for calculating volumes, surface areas, and coordinates<a>of</a>points in space. Let’s learn these essential formulas for 3D geometry.</p>
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<h2>Volume Formulas</h2>
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<h2>Volume Formulas</h2>
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<p>The volume of a solid is the amount of space it occupies.</p>
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<p>The volume of a solid is the amount of space it occupies.</p>
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<p>Here are some key volume formulas: </p>
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<p>Here are some key volume formulas: </p>
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<ul><li>Volume of a<a>cube</a>: ( V = a3 ), where ( a )is the side length. </li>
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<ul><li>Volume of a<a>cube</a>: ( V = a3 ), where ( a )is the side length. </li>
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<li>Volume of a cuboid: ( V = l ×b times h ), where ( l ), ( b ), and ( h ) are the length, breadth, and height. </li>
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<li>Volume of a cuboid: ( V = l ×b times h ), where ( l ), ( b ), and ( h ) are the length, breadth, and height. </li>
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<li>Volume of a sphere: ( V = frac{4}{3} pi r3 ), where ( r ) is the radius. </li>
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<li>Volume of a sphere: ( V = frac{4}{3} pi r3 ), where ( r ) is the radius. </li>
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<li>Volume of a cylinder: ( V = pi r2 h ), where ( r ) is the radius, and ( h ) is the height. </li>
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<li>Volume of a cylinder: ( V = pi r2 h ), where ( r ) is the radius, and ( h ) is the height. </li>
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<li>Volume of a cone: ( V = frac{1}{3} pi r2 h ).</li>
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<li>Volume of a cone: ( V = frac{1}{3} pi r2 h ).</li>
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</ul><h2>Surface Area Formulas</h2>
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</ul><h2>Surface Area Formulas</h2>
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<p>The surface area of a solid is the total area of its outer surfaces. Key surface area formulas include:</p>
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<p>The surface area of a solid is the total area of its outer surfaces. Key surface area formulas include:</p>
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<ul><li>Surface area of a cube: ( SA = 6a2 ). </li>
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<ul><li>Surface area of a cube: ( SA = 6a2 ). </li>
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<li>Surface area of a cuboid: ( SA = 2(lb + bh + hl) ). </li>
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<li>Surface area of a cuboid: ( SA = 2(lb + bh + hl) ). </li>
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<li>Surface area of a sphere: ( SA = 4 pi r2 ). </li>
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<li>Surface area of a sphere: ( SA = 4 pi r2 ). </li>
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<li>Surface area of a cylinder: ( SA = 2 pi r(h + r) ). </li>
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<li>Surface area of a cylinder: ( SA = 2 pi r(h + r) ). </li>
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<li>Surface area of a cone: ( SA = pi r(l + r) ), where ( l ) is the slant height.</li>
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<li>Surface area of a cone: ( SA = pi r(l + r) ), where ( l ) is the slant height.</li>
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</ul><h3>Explore Our Programs</h3>
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</ul><h3>Explore Our Programs</h3>
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<h2>Coordinate Geometry in 3D</h2>
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<h2>Coordinate Geometry in 3D</h2>
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<p>In 3D coordinate geometry, we use coordinates to locate points in space. Key formulas include: -</p>
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<p>In 3D coordinate geometry, we use coordinates to locate points in space. Key formulas include: -</p>
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<p>Distance between two points ((x_1, y_1, z_1)) and ((x_2, y_2, z_2)): ( d = sqrt{(x_2-x_1)2 + (y_2-y_1)2 + (z_2-z_1)2} ). -</p>
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<p>Distance between two points ((x_1, y_1, z_1)) and ((x_2, y_2, z_2)): ( d = sqrt{(x_2-x_1)2 + (y_2-y_1)2 + (z_2-z_1)2} ). -</p>
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<p>Section formula for a point dividing a line segment in the<a>ratio</a>( m:n ): ((frac{mx_2+nx_1}{m+n}, frac{my_2+ny_1}{m+n}, frac{mz_2+nz_1}{m+n})). -</p>
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<p>Section formula for a point dividing a line segment in the<a>ratio</a>( m:n ): ((frac{mx_2+nx_1}{m+n}, frac{my_2+ny_1}{m+n}, frac{mz_2+nz_1}{m+n})). -</p>
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<p>Equation of a plane in normal form: ( ax + by + cz = d ).</p>
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<p>Equation of a plane in normal form: ( ax + by + cz = d ).</p>
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<h2>Importance of 3D Geometry Formulas</h2>
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<h2>Importance of 3D Geometry Formulas</h2>
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<p>In mathematics and real-world applications, 3D geometry formulas are crucial for analyzing and understanding spatial structures.</p>
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<p>In mathematics and real-world applications, 3D geometry formulas are crucial for analyzing and understanding spatial structures.</p>
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<p>Understanding these formulas aids in: </p>
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<p>Understanding these formulas aids in: </p>
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<ul><li>Calculating the volumes and surface areas of various solids in engineering and architecture. </li>
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<ul><li>Calculating the volumes and surface areas of various solids in engineering and architecture. </li>
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<li>Solving problems in physics related to motion and forces in three dimensions. </li>
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<li>Solving problems in physics related to motion and forces in three dimensions. </li>
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<li>Modeling and interpreting<a>data</a>in fields like computer graphics and virtual reality.</li>
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<li>Modeling and interpreting<a>data</a>in fields like computer graphics and virtual reality.</li>
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</ul><h2>Tips and Tricks to Memorize 3D Geometry Formulas</h2>
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</ul><h2>Tips and Tricks to Memorize 3D Geometry Formulas</h2>
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<p>Many students find 3D geometry formulas challenging.</p>
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<p>Many students find 3D geometry formulas challenging.</p>
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<p>Here are some tips to master them: </p>
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<p>Here are some tips to master them: </p>
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<ul><li>Visualize each shape and relate it to real-world objects to understand its dimensions better. </li>
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<ul><li>Visualize each shape and relate it to real-world objects to understand its dimensions better. </li>
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<li>Use mnemonic devices to remember the order of<a>terms</a>in formulas, such as "Pi r squared height" for the volume of a cylinder. </li>
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<li>Use mnemonic devices to remember the order of<a>terms</a>in formulas, such as "Pi r squared height" for the volume of a cylinder. </li>
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<li>Create flashcards with diagrams and formulas to reinforce memory through repetition.</li>
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<li>Create flashcards with diagrams and formulas to reinforce memory through repetition.</li>
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</ul><h2>Common Mistakes and How to Avoid Them While Using 3D Geometry Formulas</h2>
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</ul><h2>Common Mistakes and How to Avoid Them While Using 3D Geometry Formulas</h2>
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<p>Students often make errors when applying 3D geometry formulas. Here are some common mistakes and tips to avoid them.</p>
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<p>Students often make errors when applying 3D geometry formulas. Here are some common mistakes and tips to avoid them.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Find the volume of a cube with side length 4 cm.</p>
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<p>Find the volume of a cube with side length 4 cm.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The volume is 64 cm³</p>
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<p>The volume is 64 cm³</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the volume, use the formula ( V = a3 ).</p>
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<p>To find the volume, use the formula ( V = a3 ).</p>
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<p>Given side length ( a = 4 ) cm,</p>
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<p>Given side length ( a = 4 ) cm,</p>
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<p>Volume ( V = 43 = 64 ) cm³.</p>
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<p>Volume ( V = 43 = 64 ) cm³.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>Calculate the surface area of a sphere with a radius of 5 cm.</p>
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<p>Calculate the surface area of a sphere with a radius of 5 cm.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The surface area is 314 cm²</p>
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<p>The surface area is 314 cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the surface area, use the formula ( SA = 4 pi r2 ).</p>
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<p>To find the surface area, use the formula ( SA = 4 pi r2 ).</p>
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<p>Given radius ( r = 5 ) cm,</p>
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<p>Given radius ( r = 5 ) cm,</p>
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<p>Surface area ( SA = 4 pi (5)2 = 314 ) cm² (approximating (pi) as 3.14).</p>
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<p>Surface area ( SA = 4 pi (5)2 = 314 ) cm² (approximating (pi) as 3.14).</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Find the distance between points (1, 2, 3) and (4, 6, 8) in 3D space.</p>
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<p>Find the distance between points (1, 2, 3) and (4, 6, 8) in 3D space.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The distance is 7 units</p>
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<p>The distance is 7 units</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the distance, use the formula ( d = sqrt{(x_2-x_1)2 + (y_2-y_1)2 + (z_2-z_1)2} ).</p>
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<p>To find the distance, use the formula ( d = sqrt{(x_2-x_1)2 + (y_2-y_1)2 + (z_2-z_1)2} ).</p>
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<p>Substitute the given coordinates: ( d = sqrt{(4-1)2 + (6-2)2 + (8-3)2} = sqrt{32 + 42 + 52} = sqrt{9 + 16 + 25} = sqrt{50} approx 7 ) units.</p>
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<p>Substitute the given coordinates: ( d = sqrt{(4-1)2 + (6-2)2 + (8-3)2} = sqrt{32 + 42 + 52} = sqrt{9 + 16 + 25} = sqrt{50} approx 7 ) units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>Find the volume of a cylinder with radius 3 cm and height 7 cm.</p>
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<p>Find the volume of a cylinder with radius 3 cm and height 7 cm.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The volume is 198 cm³</p>
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<p>The volume is 198 cm³</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the volume, use the formula ( V = pi r2 h ).</p>
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<p>To find the volume, use the formula ( V = pi r2 h ).</p>
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<p>Given radius ( r = 3 ) cm and height ( h = 7 ) cm,</p>
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<p>Given radius ( r = 3 ) cm and height ( h = 7 ) cm,</p>
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<p>Volume ( V = pi (3)2 (7) = 198 ) cm³ (approximating (pi) as 3.14).</p>
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<p>Volume ( V = pi (3)2 (7) = 198 ) cm³ (approximating (pi) as 3.14).</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Calculate the surface area of a cuboid with dimensions 2 cm by 3 cm by 4 cm.</p>
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<p>Calculate the surface area of a cuboid with dimensions 2 cm by 3 cm by 4 cm.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The surface area is 52 cm²</p>
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<p>The surface area is 52 cm²</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the surface area, use the formula ( SA = 2(lb + bh + hl) ).</p>
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<p>To find the surface area, use the formula ( SA = 2(lb + bh + hl) ).</p>
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<p>Given ( l = 2 ) cm, ( b = 3 ) cm, ( h = 4 ) cm,</p>
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<p>Given ( l = 2 ) cm, ( b = 3 ) cm, ( h = 4 ) cm,</p>
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<p>Surface area ( SA = 2(2 times 3 + 3 times 4 + 4 times 2) = 2(6 + 12 + 8) = 52 ) cm².</p>
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<p>Surface area ( SA = 2(2 times 3 + 3 times 4 + 4 times 2) = 2(6 + 12 + 8) = 52 ) cm².</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on 3D Geometry Formulas</h2>
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<h2>FAQs on 3D Geometry Formulas</h2>
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<h3>1.What is the volume formula for a sphere?</h3>
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<h3>1.What is the volume formula for a sphere?</h3>
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<p>The formula to find the volume of a sphere is ( V = frac{4}{3} pi r3 ).</p>
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<p>The formula to find the volume of a sphere is ( V = frac{4}{3} pi r3 ).</p>
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<h3>2.How do you find the surface area of a cone?</h3>
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<h3>2.How do you find the surface area of a cone?</h3>
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<p>The formula for the surface area of a cone is ( SA = pi r(l + r) ), where ( l ) is the slant height.</p>
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<p>The formula for the surface area of a cone is ( SA = pi r(l + r) ), where ( l ) is the slant height.</p>
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<h3>3.What is the distance formula in 3D geometry?</h3>
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<h3>3.What is the distance formula in 3D geometry?</h3>
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<p>The distance formula between two points ((x_1, y_1, z_1)) and ((x_2, y_2, z_2)) is ( d = sqrt{(x_2-x_1)2 + (y_2-y_1)2 + (z_2-z_1)2}z).</p>
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<p>The distance formula between two points ((x_1, y_1, z_1)) and ((x_2, y_2, z_2)) is ( d = sqrt{(x_2-x_1)2 + (y_2-y_1)2 + (z_2-z_1)2}z).</p>
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<h3>4.How do you find the volume of a cone?</h3>
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<h3>4.How do you find the volume of a cone?</h3>
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<p>The volume of a cone is found using the formula ( V = frac{1}{3} pi r2 h ).</p>
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<p>The volume of a cone is found using the formula ( V = frac{1}{3} pi r2 h ).</p>
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<h3>5.What is the section formula in 3D geometry?</h3>
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<h3>5.What is the section formula in 3D geometry?</h3>
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<p>The section formula for a point dividing a line segment in the ratio ( m:n ) is ((frac{mx_2+nx_1}{m+n}, frac{my_2+ny_1}{m+n}, frac{mz_2+nz_1}{m+n})).</p>
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<p>The section formula for a point dividing a line segment in the ratio ( m:n ) is ((frac{mx_2+nx_1}{m+n}, frac{my_2+ny_1}{m+n}, frac{mz_2+nz_1}{m+n})).</p>
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<h2>Glossary for 3D Geometry Formulas</h2>
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<h2>Glossary for 3D Geometry Formulas</h2>
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<ul><li><strong>Volume:</strong>The amount of space occupied by a solid. Calculated using formulas specific to each shape.</li>
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<ul><li><strong>Volume:</strong>The amount of space occupied by a solid. Calculated using formulas specific to each shape.</li>
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</ul><ul><li><strong>Surface Area:</strong>The total area of the external surfaces of a solid. Different shapes have specific formulas.</li>
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</ul><ul><li><strong>Surface Area:</strong>The total area of the external surfaces of a solid. Different shapes have specific formulas.</li>
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</ul><ul><li><strong>3D Coordinates:</strong>A system to specify the position of a point in space using three values (x, y, z).</li>
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</ul><ul><li><strong>3D Coordinates:</strong>A system to specify the position of a point in space using three values (x, y, z).</li>
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</ul><ul><li><strong>Slant Height:</strong>The diagonal height along the side of a cone or pyramid, used in surface area calculations.</li>
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</ul><ul><li><strong>Slant Height:</strong>The diagonal height along the side of a cone or pyramid, used in surface area calculations.</li>
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</ul><ul><li><strong>Plane Equation:</strong>An<a>equation</a>representing a flat surface in 3D space, typically expressed as ( ax + by + cz = d ).</li>
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</ul><ul><li><strong>Plane Equation:</strong>An<a>equation</a>representing a flat surface in 3D space, typically expressed as ( ax + by + cz = d ).</li>
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</ul><h2>Jaskaran Singh Saluja</h2>
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</ul><h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>