Volume and Surface Area Quiz: Test Your Geometry Skills

Question 1

Identify the shape that is NOT a lateral surface of a square pyramid.

Accepted Answer

Circle

Answer

Triangle

Answer

Square

Answer

Rectangle

Question 2

A rectangular prism has a base area of 30 cm² and a height of 5 cm. Calculate its volume.

Accepted Answer

150 cm³

Answer

15 cm³

Answer

60 cm³

Answer

300 cm³

Question 3

Identify a characteristic of a prism.

Accepted Answer

Two parallel bases connected by lateral faces

Answer

Triangular base and square lateral faces

Answer

Curved surface with a single vertex

Answer

Spherical shape with no edges

Question 4

Calculate the volume of a pyramid with square base side length (s) and height (h).

Accepted Answer

V = (1/3)s²h

Answer

V = (1/6)s²h

Answer

V = s²h

Answer

V = (1/2)s²h

Question 5

Which of the following is not a unit of volume?

Accepted Answer

Square centimeters

Answer

Cubic inches

Answer

Gallons

Answer

Liters

Question 6

Calculate the lateral surface area of a cone with radius (r) and slant height (l).

Accepted Answer

πrl

Answer

2πrl

Answer

πr²l

Answer

πrl²

Question 7

Identify the correct formula for the surface area of a sphere with radius (r).

Accepted Answer

4πr²

Answer

2πr²

Answer

πr²

Answer

3πr²

Question 8

Determine the formula for the total surface area of a rectangular prism with length (l), width (w), and height (h).

Accepted Answer

2(lw+lh+wh)

Answer

lw+lh+wh

Answer

2lw+2lh+2wh

Answer

lw*lh*wh

Question 9

The surface area of a sphere is given by the formula:

Accepted Answer

4πr²

Answer

2πr² + 2πrl

Answer

πr² - πrl

Answer

2πr² - 2πrl

Question 10

Which of the following is NOT a unit of volume?

Accepted Answer

Square meters (m²)

Answer

Cubic centimeters (cm³)

Answer

Liters (L)

Answer

Cubic feet (ft³)

Question 11

What is the total surface area of a triangular prism with a base length of 6 cm, a base width of 4 cm, and a height of 5 cm?

Accepted Answer

98 cm²

Answer

70 cm²

Answer

84 cm²

Answer

112 cm²

Question 12

What is the surface area of a sphere with a diameter of 10 cm?

Accepted Answer

100π cm²

Answer

50π cm²

Answer

25π cm²

Answer

200π cm²

Question 13

Which of the following factors does NOT affect the volume of a 3D shape?

Accepted Answer

Thickness

Answer

Length

Answer

Width

Answer

Height

Question 14

Which unit is commonly used to measure volume?

Accepted Answer

Cubic centimeters (cm³)

Answer

Square meters (m²)

Answer

Liters (L)

Answer

Grams (g)

Question 15

Which formula calculates the volume of a rectangular prism with length L, width W, and height H?

Accepted Answer

V = L x W x H

Answer

V = 2(LW + LH + WH)

Answer

V = πr²h

Answer

V = (4/3)πr³

Question 16

Which formula calculates the volume of a rectangular prism?

Accepted Answer

V = lwh

Answer

V = πr²h

Answer

V = (1/3)πr²h

Answer

V = 4/3πr³

Question 17

Calculate the surface area of a sphere with radius r.

Accepted Answer

SA = 4πr²

Answer

SA = 2πr²

Answer

SA = πr³

Answer

SA = (4/3)πr³

Question 18

Which solid has the greatest surface area for a given volume?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 19

Which formula calculates the lateral surface area of a cylinder?

Accepted Answer

LSA = 2πrh

Answer

LSA = πr²h

Answer

LSA = 2πr³

Answer

LSA = (4/3)πr³

Question 20

Which of these is not a polyhedron?

Accepted Answer

Sphere

Answer

Cube

Answer

Pyramid

Answer

Cylinder

Question 21

Determine the surface area of a cube with a side length of 4 cm.

Accepted Answer

96 cm²

Answer

16 cm²

Answer

64 cm²

Answer

256 cm²

Question 22

What is the formula for the volume of a rectangular prism?

Accepted Answer

V = l × w × h

Answer

V = π × r^2 × h

Answer

V = (4/3)π × r^3

Answer

V = s^3

Question 23

Which of the following is not a formula for calculating the volume of a cone?

Accepted Answer

V = s^3

Answer

V = (1/3)π × r^2 × h

Answer

V = (4/3)π × r^3

Answer

V = π × r^2 × h

Question 24

Identify the lateral surface area of a cylinder.

Accepted Answer

2πr × h

Answer

πr × h

Answer

4πr^2

Answer

2πr^2

Question 25

Calculate the volume of a cone with a radius of 4 cm and a height of 8 cm.

Accepted Answer

64π cm^3

Answer

32π cm^3

Answer

96π cm^3

Answer

128π cm^3

Question 26

Which formula accurately represents the volume of a rectangular prism?

Accepted Answer

V = l x w x h

Answer

V = πr²h

Answer

V = 1/3πr³

Answer

V = 4/3πr³

Question 27

The formula for calculating the lateral surface area of a cylinder is:

Accepted Answer

SA = 2πrh

Answer

SA = πr²h

Answer

SA = 4πr²

Answer

SA = 2πr³

Question 28

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

Accepted Answer

V = 200π cm³

Answer

V = 100π cm³

Answer

V = 300π cm³

Answer

V = 400π cm³

Question 29

Which of the provided options is NOT a formula for the surface area of a sphere?

Accepted Answer

SA = 1/3πr²h

Answer

SA = 4πr²

Answer

SA = 2πr² + 2πrh

Answer

SA = πr²h

Question 30

Find the volume of a rectangular prism with a length of 5 centimeters, a width of 3 centimeters, and a height of 4 centimeters.

Accepted Answer

60 cm³

Answer

20 cm³

Answer

12 cm³

Answer

10 cm³

Question 31

Which of the following is equivalent to the formula for the volume of a cone?

Accepted Answer

πr²h/3

Answer

4/3πr³

Answer

πr(r+h)/2

Answer

2πrh

Question 32

A pyramid has a square base with a side length of 6 centimeters and a height of 10 centimeters. Find its volume.

Accepted Answer

240 cm³

Answer

120 cm³

Answer

360 cm³

Answer

60 cm³

Question 33

A water tank in the shape of a rectangular prism has dimensions of 2 meters x 3 meters x 4 meters. How many liters of water can it hold?

Accepted Answer

24000 L

Answer

24 m³

Answer

240 m³

Answer

2400 L

Question 34

Which of the following is true about the volume of a sphere?

Accepted Answer

It is directly proportional to the square of the radius.

Answer

It is directly proportional to the radius.

Answer

It is inversely proportional to the radius.

Answer

It is not related to the radius.

Question 35

Find the total surface area of a cube with an edge length of 4 cm. Provide your answer in square centimeters.

Accepted Answer

64 cm²

Answer

16 cm²

Answer

32 cm²

Answer

96 cm²

Question 36

Which formula correctly calculates the volume of a pyramid?

Accepted Answer

V = (1/3)Bh

Answer

V = Bh

Answer

V = (1/2)Bh

Answer

V = B²h

Question 37

Calculate the volume of a hemisphere with a radius of 5 cm. Provide your answer in terms of π and cubic centimeters.

Accepted Answer

(1/2)(4/3)πr³

Answer

(1/2)(3/4)πr³

Answer

(1/3)(4/3)πr³

Answer

(1/3)(3/4)πr³

Question 38

Calculate the volume of a cone with a radius of 4 cm and a height of 6 cm.

Accepted Answer

16π cm³

Answer

32π cm³

Answer

8π cm³

Answer

64π cm³

Question 39

Find the surface area of a rectangular prism with a length of 10 cm, a width of 5 cm, and a height of 3 cm.

Accepted Answer

150 cm²

Answer

100 cm²

Answer

200 cm²

Answer

50 cm²

Question 40

A rectangular prism has a surface area of 240 cm². Its length is twice its width, and its height is half its width. Find the dimensions of the prism.

Accepted Answer

length = 20 cm, width = 10 cm, height = 5 cm

Answer

length = 15 cm, width = 7.5 cm, height = 3.75 cm

Answer

length = 12 cm, width = 6 cm, height = 3 cm

Answer

length = 10 cm, width = 5 cm, height = 2.5 cm

Question 41

A cone and a cylinder have the same base radius and height. Find the ratio of their volumes.

Accepted Answer

1:3

Answer

3:1

Answer

1:2

Answer

2:1

Question 42

A cylinder has a base radius of 2 centimeters and a height of 5 centimeters. What is its volume in cubic meters?

Accepted Answer

(π * 2² * 5 cubic centimeters) / 1,000,000 cubic meters

Answer

(π * 2² * 5 cubic centimeters) / 1,000 cubic meters

Answer

(π * 2² * 5 cubic centimeters) / 100 cubic meters

Answer

(π * 2² * 5 cubic centimeters) / 10 cubic meters

Question 43

Which formula calculates the volume of a cylinder?

Accepted Answer

V = πr²h

Answer

V = 2πrh

Answer

V = (1/3)πr³

Answer

V = (4/3)πr³

Question 44

Among a cone, a sphere, and a cube with equal radii, which shape possesses the largest surface area?

Accepted Answer

Sphere

Answer

Cone

Answer

Cube

Answer

All have equal surface areas

Question 45

Identify the formula that does NOT calculate the surface area of a sphere.

Accepted Answer

S = πr³

Answer

S = 4πr²

Answer

S = 2πr² + 2πrh

Answer

S = πd²

Question 46

Which formula calculates the volume of a pyramid?

Accepted Answer

V = (1/3)Bh

Answer

V = Bh

Answer

V = Bh/2

Answer

V = 2Bh

Question 47

Which solid has the smallest surface area for a given volume?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 48

Find the volume of a pyramid with a square base with a side length of 6 centimeters and a height of 10 centimeters.

Accepted Answer

120 cm³

Answer

60 cm³

Answer

180 cm³

Answer

360 cm³

Question 49

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

Accepted Answer

30 cubic centimeters

Answer

10 cubic centimeters

Answer

50 cubic centimeters

Answer

75 cubic centimeters

Question 50

Find the volume of a cone with a base radius of 3 centimeters and a height of 5 centimeters.

Accepted Answer

15π cubic centimeters

Answer

30π cubic centimeters

Answer

45π cubic centimeters

Answer

60π cubic centimeters

Question 51

Calculate the surface area of a square pyramid with a base side length of 6 centimeters and a slant height of 5 centimeters.

Accepted Answer

72 square centimeters

Answer

36 square centimeters

Answer

108 square centimeters

Answer

144 square centimeters

Question 52

A square pyramid has a base side length of 8 centimeters and a height of 12 centimeters. What is the volume of the pyramid?

Accepted Answer

384 cubic centimeters

Answer

256 cubic centimeters

Answer

512 cubic centimeters

Answer

640 cubic centimeters

Question 53

Which formula accurately represents the volume of a rectangular prism?

Accepted Answer

V = lwh

Answer

V = 2(lw + lh + hw)

Answer

V = πr²h

Answer

V = ⅓πr²h

Question 54

Which shape exhibits the lowest surface area to volume ratio?

Accepted Answer

Sphere

Answer

Cube

Answer

Cone

Answer

Pyramid

Question 55

Identify the formula for calculating the lateral surface area of a cone.

Accepted Answer

½πrl

Answer

πr²h

Answer

¼πr²h

Answer

⅓πr²h

Question 56

To find the volume of a rectangular prism, which formula would you use?

Accepted Answer

V = lwh

Answer

V = l²h

Answer

V = ½lw

Answer

V = 2(lw + wh + lh)

Question 57

Which of the following is incorrect regarding the properties of a cone?

Accepted Answer

Its volume is given by ½πr²h.

Answer

Its base is circular.

Answer

Its sides form a curved surface.

Answer

Its height is perpendicular to its base.

Question 58

Find the total volume of a solid consisting of a square pyramid with a base side length of 6 centimeters and a height of 8 centimeters, and a rectangular prism with dimensions 6 cm x 4 cm x 8 cm.

Accepted Answer

192 cubic centimeters

Answer

96 cubic centimeters

Answer

144 cubic centimeters

Answer

288 cubic centimeters

Question 59

What shape results from cross-sectioning a pyramid?

Accepted Answer

Triangle

Answer

Square

Answer

Circle

Answer

Rectangle

Question 60

Which of the following formulas calculates the volume of a rectangular prism?

Accepted Answer

V = l × w × h

Answer

V = (1/3) × πr^2h

Answer

V = (4/3) × πr^3

Answer

V = 2lw + 2lh + 2hw

Question 61

What is the surface area of a cylinder with radius 'r' and height 'h'?

Accepted Answer

SA = 2πr^2 + 2πrh

Answer

SA = πr^2 + 2πrh

Answer

SA = 2πr + 2πh

Answer

SA = πr^2h

Question 62

What is the volume of a cone with radius 'r' and height 'h'?

Accepted Answer

V = (1/3) × πr^2h

Answer

V = 2πr^2h

Answer

V = (4/3) × πr^3

Answer

V = πr^2h

Question 63

What is the base area of a square pyramid with side length 's'?

Accepted Answer

A = s^2

Answer

A = 2s^2

Answer

A = (1/2)s^2

Answer

A = (1/4)s^2

Question 64

Which of the following formulas calculates the volume of a sphere?

Accepted Answer

V = (4/3) × πr^3

Answer

V = (1/3) × πr^2h

Answer

V = πr^2h

Answer

V = 2πr^2 + 2πrh