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?