Volume and Surface Area Calculations: Master the Formulas for Prisms, Cylinders, Pyramids, and Cones

Question 1

A rectangular prism has dimensions of 5 cm in length, 3 cm in width, and 2 cm in height. Calculate the volume of the prism.

Accepted Answer

30 cm³

Answer

15 cm³

Answer

60 cm³

Answer

120 cm³

Question 2

Determine the volume of a right cone with a radius of 5 cm and a height of 12 cm.

Accepted Answer

200π cm³

Answer

100π cm³

Answer

400π cm³

Answer

800π cm³

Question 3

Calculate the surface area of a sphere with a radius of 4 cm.

Accepted Answer

32π cm²

Answer

16π cm²

Answer

64π cm²

Answer

128π cm²

Question 4

What is the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 3 centimeters?

Accepted Answer

96 cm²

Answer

72 cm²

Answer

120 cm²

Answer

144 cm²

Question 5

What is the volume of a cylinder with a radius of 3 centimeters and a height of 5 cm?

Accepted Answer

45π cm³

Answer

15π cm³

Answer

90π cm³

Answer

135π cm³

Question 6

What is the formula for calculating the volume of a rectangular prism with length (l), width (w), and height (h)?

Accepted Answer

V = lwh

Answer

V = 2(lw + lh + wh)

Answer

V = 4(lw + lh + wh)

Answer

V = πr²h

Question 7

What is the formula for calculating the surface area (SA) of a cube with side length (s)?

Accepted Answer

SA = 6s²

Answer

SA = 4s²

Answer

SA = 2s²

Answer

SA = 12s²

Question 8

What is the formula for calculating the slant height (l) of a cone with radius (r) and height (h)?

Accepted Answer

l = √(r² + h²)

Answer

l = r + h

Answer

l = r - h

Answer

l = 2rh

Question 9

Identify the incorrect formula for calculating the volume of a sphere.

Accepted Answer

V = (1/3)πr²h

Answer

V = (4/3)πr³

Answer

V = πr²h

Answer

V = 4πr³

Question 10

Find the volume of a triangular prism with a base area of 10 square centimeters and a height of 5 centimeters.

Accepted Answer

25 cubic centimeters

Answer

50 cubic centimeters

Answer

10 cubic centimeters

Answer

15 cubic centimeters

Question 11

Find the volume of a pyramid with a triangular base of area 12 square units and a height of 5 units.

Accepted Answer

20 cubic units

Answer

12 cubic units

Answer

60 cubic units

Question 12

Find the volume of a rectangular prism with dimensions: length = 5 cm, width = 3 cm, height = 2 cm.

Accepted Answer

30 cubic centimeters

Answer

120 cubic centimeters

Answer

60 cubic centimeters

Answer

10 cubic centimeters

Question 13

Calculate the volume of a square pyramid with a base side length of 8 centimeters and a height of 12 centimeters.

Accepted Answer

(64/3) cm³

Answer

64 cm³

Answer

(32/3) cm³

Answer

128 cm³

Question 14

A cylinder has a radius of 3 centimeters and a height of 5 centimeters. Calculate the volume of the cylinder.

Accepted Answer

45π cm³

Answer

90π cm³

Answer

15π cm³

Question 15

Calculate the volume of a rectangular prism with the following dimensions: length = 5 cm, width = 3 cm, height = 2 cm.

Accepted Answer

30 cm³

Answer

15 cm³

Answer

10 cm³

Answer

25 cm³

Question 16

Find the volume of a rectangular prism with dimensions length = 5 cm, width = 3 cm, and height = 2 cm.

Accepted Answer

30 cubic centimeters

Answer

60 cubic centimeters

Answer

20 cubic centimeters

Answer

15 cubic centimeters

Question 17

Calculate the volume of a pyramid with a square base of side length 4 units and a height of 5 units.

Accepted Answer

40/3 cubic units

Answer

20/3 cubic units

Answer

80/3 cubic units

Answer

10 cubic units

Question 18

Which of the following solids exhibits the greatest volume for a given surface area?

Accepted Answer

Sphere

Answer

Cylinder

Answer

Cube

Answer

Pyramid

Question 19

Which of the following solids possesses the smallest surface area for a given volume?

Accepted Answer

Sphere

Answer

Pyramid

Answer

Cylinder

Answer

Cube

Question 20

A cube has a side length of 7 cm. What is its surface area?

Accepted Answer

294 cm²

Answer

343 cm²

Answer

441 cm²

Answer

147 cm²

Question 21

A pyramid has a square base with side length 5 cm and a height of 12 cm. What is the volume of the pyramid?

Accepted Answer

100 cm³

Answer

50 cm³

Answer

150 cm³

Question 22

A rectangular prism has a volume of 180 cubic centimeters (cm³). If its length is 12 cm and its width is 5 cm, what is its height?

Accepted Answer

3 cm

Answer

15 cm

Answer

9 cm

Answer

6 cm

Question 23

A cylinder has a surface area of 150π square centimeters (cm²). If its radius is 5 cm, what is its height?

Accepted Answer

10 cm

Answer

5 cm

Answer

15 cm

Answer

20 cm

Question 24

A rectangular prism has a length of 10 cm, a width of 6 cm, and a height of 4 cm. A cylinder has a radius of 3 cm and a height of 10 cm. Which shape has a larger volume?

Accepted Answer

The rectangular prism

Answer

It's impossible to determine without more information.

Answer

The cylinder

Answer

They have the same volume.

Question 25

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is its volume?

Accepted Answer

120 cm³

Answer

40 cm³

Answer

96 cm³

Answer

150 cm³

Question 26

A pyramid has a square base with sides of 6 cm and a height of 8 cm. What is its volume?

Accepted Answer

96 cm³

Answer

72 cm³

Answer

144 cm³

Answer

36 cm³

Question 27

A cone has a radius of 5 cm and a height of 12 cm. What is its surface area (rounded to the nearest tenth of a square centimeter)?

Accepted Answer

282.7 cm²

Answer

157 cm²

Answer

314 cm²

Answer

196.3 cm²

Question 28

A cube has a side length of 4 cm. What is its surface area?

Accepted Answer

96 cm²

Answer

48 cm²

Answer

24 cm²

Answer

64 cm²

Question 29

A rectangular prism has a volume of 120 cm³ and a length of 6 cm and a width of 4 cm. What is its height?

Accepted Answer

5 cm

Answer

10 cm

Answer

8 cm

Answer

3 cm

Question 30

A cylinder has a surface area of 251.2 cm² and a radius of 4 cm. What is its height?

Accepted Answer

6 cm

Answer

9 cm

Answer

12 cm

Answer

3 cm

Question 31

A pyramid has a volume of 100 cm³ and a square base with sides of 5 cm. What is its height?

Accepted Answer

12 cm

Answer

10 cm

Answer

8 cm

Answer

6 cm

Question 32

A cone has a surface area of 157 cm² and a radius of 5 cm. What is its slant height?

Accepted Answer

8 cm

Answer

6 cm

Answer

10 cm

Answer

4 cm

Question 33

A rectangular prism with a length of 10 cm, a width of 5 cm, and a height of 4 cm is filled with water. If the water is poured into a cylindrical container with a radius of 5 cm, what is the height of the water in the cylinder?

Accepted Answer

4 cm

Answer

2 cm

Answer

8 cm

Answer

10 cm