Volume and Surface Area Quizzes: Test Your Understanding

Question 1

A cube has a volume of 27 cm³. What is its side length?

Accepted Answer

3 cm

Answer

6 cm

Answer

9 cm

Answer

12 cm

Question 2

Find the volume of a cube whose sides are 5 centimeters long.

Accepted Answer

125 cm³

Answer

25 cm³

Answer

250 cm³

Answer

500 cm³

Question 3

A cuboid has a length of 10 centimeters, a width of 8 centimeters, and a height of 6 centimeters. If the length and height are both doubled, calculate the new surface area.

Accepted Answer

432 square centimeters

Answer

176 square centimeters

Answer

352 square centimeters

Answer

512 square centimeters

Question 4

Which formula calculates the volume of a cube?

Accepted Answer

V = l × w × h

Answer

V = 4 × (l × w)

Answer

V = l × w

Answer

V = 6 × (l × w × h)

Question 5

Which relationship exists between the volume of a cube and the length of its side?

Accepted Answer

Volume is directly proportional to the square of the length of the side

Answer

Volume is directly proportional to the length of the side

Answer

Volume is inversely proportional to the length of the side

Answer

Volume is inversely proportional to the square of the length of the side

Question 6

What is the formula to calculate the volume of a sphere with radius 'r'?

Accepted Answer

(4/3)π * r^3

Answer

(3/4)π * r^3

Answer

4π * r^3

Answer

3π * r^3

Question 7

Which unit of measurement represents volume in the metric system?

Accepted Answer

Cm³

Answer

Cm

Answer

Cm²

Answer

Cm⁴

Question 8

Calculate the surface area of a cuboid with a length of 6 cm, a width of 4 cm, and a height of 3 cm.

Accepted Answer

72 cm²

Answer

42 cm²

Answer

54 cm²

Answer

96 cm²

Question 9

Compare the volumes of a rectangular prism with a base length of 4 cm, a base width of 3 cm, and a height of 5 cm, and a cube with an edge length of 5 cm. Which shape has the greater volume?

Accepted Answer

The cube

Answer

The rectangular prism

Answer

Both have the same volume

Answer

Cannot be determined

Question 10

What is the formula for calculating the volume of a cube with side length 'a'?

Accepted Answer

V = a^3

Answer

V = 4 * π * a^3

Answer

V = π * a^2 * h

Answer

V = 2 * π * a * r

Question 11

A cylindrical can has a radius of 2 cm and a height of 6 cm. What is its volume?

Accepted Answer

24π cm³

Answer

12π cm³

Answer

36π cm³

Answer

48π cm³

Question 12

Find the volume of a cube with a side length of 3 cm.

Accepted Answer

27 cm³

Answer

9 cm³

Answer

18 cm³

Answer

36 cm³

Question 13

Identify the formula that is NOT used to calculate the surface area of a cuboid.

Accepted Answer

lh + lh + wh

Answer

2(lw + wh + hl)

Answer

lw + wh + hl

Answer

2lh + 2wh + 2lw

Question 14

Find the surface area of a cuboid with a length of 5 cm, a width of 3 cm, and a height of 2 cm.

Accepted Answer

56 cm²

Answer

34 cm²

Answer

70 cm²

Answer

84 cm²

Question 15

A rectangular prism has a volume of 60 cm³ and a base area of 12 cm². What is its height?

Accepted Answer

5 cm

Answer

2 cm

Answer

10 cm

Answer

15 cm

Question 16

Which of the following is not a unit of volume?

Accepted Answer

Centimeter

Answer

Cubic meter

Answer

Liter

Answer

Milliliter

Question 17

What is the formula for calculating the volume of a cube?

Accepted Answer

Length x length x length

Answer

Length x width x height

Answer

2 x length x width

Answer

4 x length x width

Question 18

Which of these is NOT a unit of volume?

Accepted Answer

Square centimetres

Answer

Cubic centimetres

Answer

Cubic metres

Answer

Litres

Question 19

What is the formula for calculating the volume of a cube?

Accepted Answer

V = l^3

Answer

V = l * w * h

Answer

V = 2(lw + lh + wh)

Answer

V = 4 * l^2

Question 20

Which of the following is a unit of volume?

Accepted Answer

Cubic centimeter

Answer

Centimeter

Answer

Meter

Answer

Square meter

Question 21

A cylindrical can has a radius of 5 cm and a height of 10 cm. What is the volume of the can in cubic centimeters?

Accepted Answer

250π cm³

Answer

100π cm³

Answer

75π cm³

Answer

50π cm³

Question 22

Which formula is not used to calculate the volume of a cylinder?

Accepted Answer

V = lwh

Answer

V = πr²h

Answer

V = 4/3πr³

Answer

V = 2πrh

Question 23

Which formula is used to calculate the surface area of a sphere?

Accepted Answer

A = 4πr²

Answer

A = πr³

Answer

A = lwh

Answer

A = 2πrh

Question 24

What is the formula for calculating the volume of a cuboid?

Accepted Answer

V = l * w * h

Answer

V = 2(lw + lh + wh)

Answer

V = l + w + h

Answer

V = 1/3 * πr²h

Question 25

Calculate the surface area of a cuboid with a length of 5 cm, width of 3 cm, and height of 2 cm.

Accepted Answer

38 cm²

Answer

26 cm²

Answer

50 cm²

Answer

60 cm²

Question 26

Which unit is used to measure volume?

Accepted Answer

Cubic centimeters

Answer

Centimeters

Answer

Meters

Answer

Square meters

Question 27

A cube with a volume of 64 cm³ has a side length of:

Accepted Answer

8 cm

Answer

4 cm

Answer

6 cm

Answer

10 cm

Question 28

The formula for calculating the volume of a cube is:

Accepted Answer

V = s^3

Answer

V = s^2

Answer

V = 4s^2

Answer

V = 6s^2

Question 29

A rectangular prism has a square base with a side length of 4 cm. If the height of the prism is 6 cm, what is its volume?

Accepted Answer

96 cm³

Answer

24 cm³

Answer

48 cm³

Answer

192 cm³

Question 30

What is the difference between volume and surface area?

Accepted Answer

Volume is the amount of space inside a shape, while surface area is the area of the outside surfaces.

Answer

Surface area is the amount of space inside a shape, while volume is the area of the outside surfaces.

Answer

Volume and surface area are the same thing.

Answer

Surface area is more important than volume.

Question 31

Which of the following is NOT a factor affecting the volume of a rectangular prism?

Accepted Answer

Colour

Answer

Length

Answer

Width

Answer

Height

Question 32

A cube has a side length of 4 cm. Calculate its volume.

Accepted Answer

64 cm³

Answer

16 cm³

Answer

36 cm³

Answer

100 cm³

Question 33

A cuboid has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its total surface area?

Accepted Answer

34 cm²

Answer

20 cm²

Answer

50 cm²

Answer

70 cm²

Question 34

A garden measuring 6 m by 4 m is fenced with a 2 m high fence on all four sides. Calculate the fence's total surface area.

Accepted Answer

100 m²

Answer

20 m²

Answer

40 m²

Answer

80 m²

Question 35

What's the total surface area of a cylinder with a 3 cm radius and a 5 cm height?

Accepted Answer

90π cm²

Answer

30π cm²

Answer

60π cm²

Answer

120π cm²

Question 36

Which of the following solids has the greatest volume: a cube with a side length of 3 cm, a rectangular prism with a length of 4 cm, width of 2 cm, and height of 5 cm, or a cylinder with a radius of 2 cm and height of 6 cm?

Accepted Answer

Cylinder

Answer

Rectangular prism

Answer

Cube

Answer

All have the same volume

Question 37

A cube has a side length of 5 cm. What is its volume?

Accepted Answer

125 cm³

Answer

75 cm³

Answer

150 cm³

Answer

25 cm³

Question 38

A box in the shape of a cube has a volume of 27 cm³. What is the length of one side of the cube?

Accepted Answer

3 cm

Answer

4 cm

Answer

6 cm

Answer

9 cm

Question 39

A rectangular tank has a base area of 12 cm² and a height of 5 cm. What is the volume of the tank?

Accepted Answer

60 cm³

Answer

36 cm³

Answer

24 cm³

Answer

17 cm³

Question 40

A cube has a surface area of 96 cm². What is the length of one side of the cube?

Accepted Answer

4 cm

Answer

6 cm

Answer

8 cm

Answer

2 cm

Question 41

A cube is painted on all its faces. If the cube is then cut into 27 smaller cubes of equal size, how many of the smaller cubes have paint on exactly two of their faces?

Accepted Answer

12

Answer

8

Answer

16

Answer

20

Question 42

A cube has a side length of 5 cm. What is its volume?

Accepted Answer

125 cm³

Answer

15 cm³

Answer

25 cm²

Question 43

A cuboid has dimensions of 2 cm, 4 cm, and 6 cm. What is its surface area?

Accepted Answer

88 cm²

Answer

48 cm²

Answer

24 cm²

Answer

44 cm²

Question 44

A rectangular box needs to be wrapped with gift wrap. The box measures 10 cm by 8 cm by 5 cm. What is the minimum amount of gift wrap needed to cover the entire box?

Accepted Answer

360 cm²

Answer

230 cm²

Answer

180 cm²

Answer

400 cm²

Question 45

A swimming pool is shaped like a cuboid and measures 10 m long, 5 m wide, and 2 m deep. What is the volume of water the pool can hold?

Accepted Answer

100 m³

Answer

50 m³

Answer

20 m³

Answer

75 m³

Question 46

A cube has a volume of 64 cm³. What is the length of one of its sides?

Accepted Answer

4 cm

Answer

8 cm

Answer

32 cm

Answer

16 cm

Question 47

Two cubes have side lengths of 3 cm and 6 cm respectively. What is the ratio of their volumes?

Accepted Answer

1:8

Answer

9:36

Answer

3:6

Answer

1:2

Question 48

A rectangular prism has a volume of 120 cm³ and a base area of 20 cm². What is the height of the prism?

Accepted Answer

6 cm

Answer

12 cm

Answer

10 cm

Answer

24 cm

Question 49

A company wants to minimize the cost of packaging by reducing the surface area of its boxes. Which of the following box dimensions will result in the smallest surface area for a given volume?

Accepted Answer

5 cm x 5 cm x 5 cm

Answer

10 cm x 5 cm x 2 cm

Answer

8 cm x 4 cm x 4 cm

Question 50

A cube is painted red on all faces and then cut into 27 smaller cubes of equal size. How many of the smaller cubes will have exactly two faces painted red?

Accepted Answer

12

Answer

8

Answer

6

Answer

27

Question 51

If you double the length of all sides of a cube, what happens to its volume?

Accepted Answer

It increases by a factor of 8

Answer

It quadruples

Answer

It doubles

Answer

It increases by a factor of 16