Cube	Surface Area	6 × side2
	Volume	side3
Rectangular Prism	Surface Area	2(length × width + length × height + width × height)
	Volume	length × width × height
Cylinder	Surface Area	2π × radius(radius + height)
	Volume	π × radius2 × height
Sphere	Surface Area	4π × radius2
	Volume	(4/3)π × radius3
Cone	Surface Area	π × radius(radius + slant height)
	Volume	(1/3)π × radius2 × height
Pyramid	Surface Area	Sum of areas of all faces
	Volume	(1/3) × base area × height
Triangular Prism	Surface Area	Sum of areas of all faces
	Volume	(1/2) × base × height × length
Cuboid	Surface Area	2(length × width + length × height + width × height)
	Volume	length × width × height
Cone Frustum (or Truncated Cone)	Surface Area	π(radius1 + radius2)(slant height) + π(radius12 + radius22)
	Volume	(1/3)π(height)(radius12 + radius22 + radius1 × radius2)
Hemisphere	Curved Surface Area	2π × radius2
	Total Surface Area	3π × radius2
	Volume	(2/3)π × radius3

Surface Area Formulas

Problems on Surface Area and Volume formulas with solution

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 on Surface Area and Volume Formulas

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 radius 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?

Surface Area and Volume – FAQs

What is surface area?

Surface area is the total area that covers the outer surface of a three-dimensional object.

How is surface area different from volume?

Surface area measures the area of the object’s outer surface, while volume measures the space enclosed by the object.

What are the common units for measuring surface area and volume?

The units for measuring surface area are square units (e.g., square centimeters, square meters), while the units for volume are cubic units (e.g., cubic centimeters, cubic meters).

What are some real-life applications of surface area and volume calculations?

Surface area and volume calculations are used in various fields such as architecture, engineering, construction, and manufacturing to design and analyze objects like buildings, containers, and machinery.

How do you calculate the surface area of a cylinder?

The surface area of a cylinder is calculated by adding the areas of its two circular bases and the lateral surface area, which is the product of the height and the circumference of the base.

What is the formula for finding the volume of a sphere?

The formula for finding the volume of a sphere is

[Tex]\frac{4}{3} \pi r^3[/Tex], where r is the radius of the sphere.

How do you find the volume of a cone?

The volume of a cone can be calculated using the formula

[Tex]\frac{1}{3} \pi r^2h[/Tex], where r is the radius of the base and h is the height of the cone.

What is the relationship between the surface area and volume of an object?

Generally, as the volume of an object increases, its surface area also tends to increase. However, this relationship may vary depending on the shape and dimensions of the object.

Why is it important to calculate surface area and volume accurately?

Accurate calculations of surface area and volume are essential for designing efficient structures, optimizing material usage, and ensuring proper functionality of objects in various applications.