Practice Problems on Surface Area and Volume (original) (raw)

Last Updated : 13 Apr, 2026

Surface area is the total area of all the outer surfaces or faces of a three-dimensional object. It tells us how much area is needed to cover the surface of a solid.

Volume is the amount of space occupied inside a three-dimensional object. It represents the total space enclosed within the boundaries of the object.

These problems will help you practice and better understand the concepts of surface area and volume.

**Question 1. Calculate the surface area and volume of a cylinder with radius 6 cm and height 15 cm.

Surface Area. 2 × π × 6 × (6 + 15) + 2 × π × 62 = 792π square cm

Volume. π × 62 × 15 = 540π cubic cm

**Question 2. Find the surface area and volume of a cone with radius 8 cm and height 10 cm.

Surface Area. π × 8 × (8 + 10) + π × 82 = 392π square cm

Volume. (1/3) × π × 82 × 10 = 640π/3 cubic cm

**Question 3. Determine the surface area and volume of a sphere with radius 12 cm.

Surface Area. 4 × π × 122 = 576π square cm

Volume. (4/3) × π × 123 = 6912π cubic cm

**Question 4. Compute the surface area and volume of a cuboid with length 10 cm, width 6 cm, and height 4 cm.

Surface Area. 2 × (10 × 6 + 10 × 4 + 6 × 4) = 332 square cm

Volume. 10 × 6 × 4 = 240 cubic cm

**Question 5. What is the surface area and volume of a pyramid with base side length 14 cm and height 8 cm?

Surface Area. 4 × (1/2) × 14 × √(14/2)2 + 82 + 142 = 588 square cm

Volume. (1/3) × 142 × 8 = 448 cubic cm

**Question 6. Calculate the surface area and volume of a cylinder with radius 4 cm and height 12 cm.

Surface Area. 2 × π × 4 × (4 + 12) + 2 × π × 42 = 352π square cm

Volume. π × 42 × 12 = 192π cubic cm

**Question 7. Find the surface area and volume of a cone with radius 10 cm and height 15 cm.

Surface Area. π × 10 × (10 + 15) + π × 102 = 650π square cm

Volume. (1/3) × π × 102 × 15 = 500π cubic cm

**Question 8. Determine the surface area and volume of a sphere with a radius of 15 cm.

Surface Area. 4 × π × 152 = 900π square cm

Volume. (4/3) × π × 153 = 4500π cubic cm

**Question 9. Compute the surface area and volume of a cuboid with length 8 cm, width 5 cm, and height 6 cm.

Surface Area. 2 × (8 × 5 + 8 × 6 + 5 × 6) = 316 square cm

Volume. 8 × 5 × 6 = 240 cubic cm

**Question 10. What is the surface area and volume of a pyramid with base side length 12 cm and height 10 cm?

Surface Area. 4 × (1/2) × 12 × √(12/2)2 + 102 + 122 = 432 square cm

Volume. (1/3) × 122 × 10 = 480 cubic cm

**Question 11. A cylindrical container has a radius of 5 cm and a height of 10 cm. Calculate the total surface area and volume of the container.

Surface Area. 2π × 5 × (5 + 10) + 2π × 52 = 350π square cm

Volume. π × 52 × 10 = 250π cubic cm

**Question 12. A conical tank has a radius of 8 m and a height of 12 m. Determine the total surface area and volume of the tank.

Surface Area. π × 8 × (8 + 12) + π × 82 = 560π square m

Volume. (1/3) × π × 82 × 12 = 640π cubic m

**Question 13. A spherical water tank has a radius of 15 m. Find the total surface area and volume of the tank.

Surface Area. 4π × 152 = 900π square m

Volume. (4/3) × π × 153 = 9000π cubic m

**Question 14. A rectangular prism-shaped bookshelf measures 1.5 m in length, 1 m in width, and 2 m in height. Calculate its total surface area and volume.

Surface Area. 2 × (1.5 × 1 + 1.5 × 2 + 1 × 2) = 11 square m

Volume. 1.5 × 1 × 2 = 3 cubic m

**Question 15. A pyramid-shaped tent has a square base with side length 10 m and a height of 8 m. Determine its total surface area and volume.

Surface Area. 4 × (1/2) × 10 × √((10/2)2 + 82) + 102 = 300 square m

Volume. (1/3) × 102 × 8 = 266.67 cubic m

**Question 16. A cylindrical tank has a diameter of 6 ft and a height of 14 ft. Calculate the total surface area and volume of the tank.

Surface Area. 2π × 3 × (3 + 14) + 2π × 32 = 312π square ft

Volume. π × 32 × 14 = 126π cubic ft

**Question 17. A cone-shaped funnel has a radius of 4 cm and a slant height of 10 cm. Determine its total surface area and volume.

Surface Area. π × 4 × (4 + 10) + π × 42 = 240π square cm

Volume. (1/3) × π × 42 × 10 = 160π cubic cm

Practice Problems

**Q1. Calculate the surface area and volume of a cylinder with radius 5 cm and height 12 cm.

**Q2. Find the surface area and volume of a cone with radius 10 cm and height 15 cm.

**Q3. Determine the surface area and volume of a sphere with a radius of 8 cm.

**Q4. Compute the surface area and volume of a cuboid with length 6 cm, width 8 cm, and height 10 cm.

**Q5. What is the surface area and volume of a pyramid with base side length 12 cm and height 9 cm?

**Q6. Calculate the surface area and volume of a cylinder with radius 3 cm and height 10 cm.

**Q7. Find the surface area and volume of a cone with radius 7 cm and height 12 cm.

**Q8. Determine the surface area and volume of a sphere with radius 15 cm.

**Q9. Compute the surface area and volume of a cuboid with length 4 cm, width 6 cm, and height 8 cm.

**Q10. What is the surface area and volume of a pyramid with base side length 10 cm and height 6 cm?