Volume and Surface Area: Master 3D Shape Measurements

Question 1

Which formula accurately calculates the surface area of a cone?

Accepted Answer

πr² + πrl

Answer

4πr²

Answer

2πrl

Answer

πr² - πrl

Question 2

Which property is NOT applicable to a pyramid?

Accepted Answer

Volume is equivalent to one-third the volume of a prism with the same base and height

Answer

Possesses a polygonal base

Answer

Contains a single vertex

Answer

Composed of triangular faces

Question 3

Calculate the volume of a cone with a base radius of 2 centimeters (cm) and a slant height of 5 cm. Express your answer in cubic centimeters (cm³).

Accepted Answer

20π cm³

Answer

10π cm³

Answer

30π cm³

Answer

40π cm³

Question 4

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

Accepted Answer

4πr²

Answer

πr²

Answer

2πrl

Answer

πr³

Question 5

What's the formula for calculating the volume of a rectangular prism?

Accepted Answer

V = l * w * h

Answer

V = 1/2 * b * h

Answer

V = 4/3 * πr³

Answer

V = 2 * (l * w + w * h + h * l)

Question 6

What's the formula for calculating the surface area of a cylinder?

Accepted Answer

SA = 2πr² + 2πrh

Answer

SA = πr²

Answer

SA = 4/3 * πr³

Answer

SA = l * w * h

Question 7

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

Accepted Answer

15 cubic cm

Answer

10 cubic cm

Answer

30 cubic cm

Answer

60 cubic cm

Question 8

What's the formula for calculating the volume of a sphere?

Accepted Answer

V = 4/3 * πr³

Answer

V = 1/2 * πr²

Answer

V = πr³

Answer

V = 2 * πr² + 2πrh

Question 9

Calculate the volume of a cylinder with a radius of 3 cm and a height of 5 cm.

Accepted Answer

30π cm³

Answer

15π cm³

Answer

45π cm³

Answer

60π cm³

Question 10

Which of the following surfaces is NOT considered a lateral surface?

Accepted Answer

The base of a prism

Answer

The sides of a pyramid

Answer

The top of a cylinder

Answer

The curved surface of a cone

Question 11

Which of the following units is used to measure volume?

Accepted Answer

Cubic centimeter (cm³)

Answer

Centimeter (cm)

Answer

Meter (m)

Answer

Square centimeter (cm²)

Question 12

Which of the following properties is NOT characteristic of surface area?

Accepted Answer

It can be zero.

Answer

It is a measure of the outer boundary of an object.

Answer

It is always expressed in square units.

Answer

It is additive.

Question 13

A cube with a side length of 5 cm has a surface area of:

Accepted Answer

100 cm²

Answer

25 cm²

Answer

50 cm²

Answer

150 cm²

Question 14

A cylinder has a radius of 3 cm and a height of 10 cm. What is its volume?

Accepted Answer

90π cm³

Answer

27π cm³

Answer

270π cm³

Answer

900π cm³

Question 15

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 5 cm. What is its surface area?

Accepted Answer

138 cm²

Answer

46 cm²

Answer

92 cm²

Answer

230 cm²

Question 16

Which of the following is a unit of volume?

Accepted Answer

Cubic meter

Answer

Square centimeter

Answer

Meter

Answer

Kilogram

Question 17

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

Accepted Answer

(1/3)πr²h

Answer

πr²h

Answer

2πrh

Answer

4/3πr³

Question 18

Find the volume of a rectangular pyramid with a base length of 6 cm, a base width of 4 cm, and a height of 5 cm.

Accepted Answer

40 cm³

Answer

20 cm³

Answer

60 cm³

Answer

80 cm³

Question 19

Determine the formula used to calculate the volume of a cube.

Accepted Answer

V = s³

Answer

V = 2s³

Answer

V = s² * h

Answer

V = 4s³

Question 20

Calculate the surface area of a sphere with a radius of 5 centimeters.

Accepted Answer

100π cm²

Answer

25π cm²

Answer

50π cm²

Answer

200π cm²

Question 21

Identify the net that, when folded, forms a cube.

Accepted Answer

[Image of a net for a cube]

Answer

[Image of a net for a square pyramid]

Answer

[Image of a net for a rectangular prism]

Answer

[Image of a net for a triangular prism]

Question 22

Calculate the surface area of a cylinder with a base radius of 4 centimeters and a height of 10 centimeters.

Accepted Answer

64π cm²

Answer

32π cm²

Answer

128π cm²

Answer

96π cm²

Question 23

Identify the shape that maximizes volume for a given surface area.

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 24

Find the volume of a rectangular prism with a length of 10 centimeters, a width of 5 centimeters, and a height of 3 centimeters.

Accepted Answer

60 cm³

Answer

15 cm³

Answer

30 cm³

Answer

180 cm³

Question 25

Calculate the volume of a cone with a radius of 4 cm and a height of 6 cm. Use the formula V = (1/3)πr²h.

Accepted Answer

64π cm³

Answer

32π cm³

Answer

96π cm³

Answer

128π cm³

Question 26

A rectangular prism has a length of 8 cm, a width of 5 cm, and a volume of 200 cm³. Calculate its height.

Accepted Answer

6 cm

Answer

5 cm

Answer

8 cm

Answer

10 cm

Question 27

Which of the following shapes has the smallest surface area to volume ratio?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 28

Identify the solid that is NOT a prism:

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Triangular prism

Question 29

Calculate the volume of a cone with a radius of 5 cm and a height of 10 cm.

Accepted Answer

100π cm³

Answer

50π cm³

Answer

150π cm³

Answer

250π cm³