Surface Areas and Volumes Solved Examples (Class 10 Mathematics)
Calculate surface areas and volumes of 3D solids including cubes, cylinders, cones, and spheres. These problems combine geometry with practical application
TL;DR: Calculate surface areas and volumes of 3D solids including cubes, cylinders, cones, and spheres. These problems combine geometry with practical applic…
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Calculate surface areas and volumes of 3D solids including cubes, cylinders, cones, and spheres. These problems combine geometry with practical application
Surface Areas and Volumes — Solved Numerical Examples (Step by Step)
Example 1: Find the surface area and volume of a cube with side 5 cm.
Solution: Surface area of cube = 6a² = 6 × 5² = 6 × 25 = 150 cm²
Volume of cube = a³ = 5³ = 125 cm³
Example 2: A cylinder has radius 7 cm and height 10 cm. Find its total surface area.
Solution: Total surface area = 2πr(r + h) = 2 × (22/7) × 7 × (7 + 10) = 2 × 22 × 17 = 748 cm²
Example 3: Find the volume of a cone with base radius 3 cm and height 8 cm.
Solution: Volume of cone = (1/3)πr²h = (1/3) × (22/7) × 3² × 8 = (1/3) × (22/7) × 9 × 8
= (22 × 9 × 8) / (3 × 7) = (22 × 72) / 21 = 1584 / 21 = 75.43 cm³
Example 4: A sphere has radius 7 cm. Calculate its surface area and volume.
Solution: Surface area = 4πr² = 4 × (22/7) × 7² = 4 × 22 × 7 = 616 cm²
Volume = (4/3)πr³ = (4/3) × (22/7) × 7³ = (4/3) × 22 × 49 = (4 × 22 × 49) / 3 = 4312 / 3 = 1437.33 cm³
Example 5: A hemispherical bowl has radius 10 cm. What is its curved surface area?
Solution: Curved surface area of hemisphere = 2πr² = 2 × (22/7) × 10² = 2 × (22/7) × 100 = 4400/7 = 628.57 cm²
Example 6: A rectangular prism has dimensions 8 cm × 6 cm × 4 cm. Find its volume and surface area.
Solution: Volume = l × b × h = 8 × 6 × 4 = 192 cm³
Surface area = 2(lb + bh + lh) = 2(8×6 + 6×4 + 8×4) = 2(48 + 24 + 32) = 2 × 104 = 208 cm²
Tips
- For any 3D solid, visualize it and identify all surfaces that contribute to total surface area.
- Curved surface area excludes the bases; total surface area includes all surfaces.
- Use π = 22/7 for exact answers in problems; π ≈ 3.14 for approximate calculations.
Frequently Asked Questions
What is the difference between curved surface area and total surface area?
Curved surface area includes only the curved/lateral surfaces. Total surface area includes curved surfaces plus all flat bases.
How do you find the slant height of a cone?
If radius r and height h are known, slant height l = √(r² + h²) using the Pythagorean theorem.
More Mathematics Solved Examples
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