Volume and Surface Area: Master 3D Shape Calculations

Question 1

Which expression does NOT represent the surface area of a cube?

Accepted Answer

4s³

Answer

6s²

Answer

s³

Answer

2s(s + s)

Question 2

Determine the volume of a cylinder with a radius of 4 cm and a height of 6 cm.

Accepted Answer

48π cm³

Answer

24π cm³

Answer

96π cm³

Answer

144π cm³

Question 3

Which expression does NOT represent the surface area of a pyramid?

Accepted Answer

B(h + ℓ)/2

Answer

½Pℓ

Answer

Bs + ½Pℓ

Answer

B + ½Pℓ

Question 4

Choose the correct expression for the base area of a cone.

Accepted Answer

πr²

Answer

πrs

Answer

2πrs

Answer

πr(r + s)

Question 5

Which option is NOT a property of a sphere?

Accepted Answer

Has two congruent bases

Answer

Has a single radius

Answer

Has a single diameter

Answer

Has a curved surface

Question 6

Identify the common features between the volume formulas for a cylinder and a cone.

Accepted Answer

Both formulas use the area of the base.

Accepted Answer

Both formulas use the height of the shape.

Accepted Answer

Both formulas use the mathematical constant pi (π).

Question 7

The formula for the volume of a cone is V = 1/3πr²h. What does each term in this formula represent?

Accepted Answer

r: radius of the base, h: height, π: constant approximately equal to 3.14

Answer

r: radius of the top, h: slant height, π: variable that can change

Answer

r: height, h: radius of the base, π: constant approximately equal to 22/7

Answer

r: radius of the base, h: diameter, π: constant representing the ratio of a circle's circumference to its diameter

Question 8

A cube and a sphere have the same volume. Which shape has a greater surface area? Explain your reasoning.

Accepted Answer

The sphere has a greater surface area.

Answer

The cube has a greater surface area.

Answer

The cube and sphere have the same surface area.

Question 9

Calculate the volume and surface area of a rectangular prism with a length of 5 cm, a width of 3 cm, and a height of 2 cm. Explain how these values are connected to the prism's dimensions.

Accepted Answer

Volume: 30 cm³, Surface Area: 60 cm², Related to dimensions by multiplication

Answer

Volume: 60 cm³, Surface Area: 30 cm², Related to dimensions by addition

Answer

Volume: 5 cm³, Surface Area: 30 cm², Related to dimensions by division

Answer

Volume: 30 cm³, Surface Area: 120 cm², Related to dimensions by subtraction

Question 10

Which of the following formulas calculates the volume of a cone accurately?

Accepted Answer

V = (1/3)πr²h

Answer

V = πr²(2h)

Answer

V = (4/3)πr³

Answer

V = πr²l

Question 11

Which of the following solids lacks lateral faces?

Accepted Answer

Sphere

Answer

Cube

Answer

Prism

Answer

Cone

Question 12

A cone has a slant height of 10 cm and a radius of 6 cm. Calculate its surface area.

Accepted Answer

120π cm²

Answer

60π cm²

Answer

180π cm²

Answer

240π cm²

Question 13

Which of the following formulas is used to calculate the surface area of a prism?

Accepted Answer

SA = 2(lw + lh + hw)

Answer

SA = πr² + πrl

Answer

SA = 4πr²

Answer

SA = (4/3)πr³

Question 14

Find the volume of a pyramid with a square base of side length 6 cm and a height of 8 cm.

Accepted Answer

48 cubic centimeters

Answer

16 cubic centimeters

Answer

32 cubic centimeters

Answer

64 cubic centimeters

Question 15

Which shape exhibits the smallest surface area for a given volume?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 16

Which factor does NOT influence the volume of a 3D shape?

Accepted Answer

Color of the shape

Answer

Base area

Answer

Height

Answer

Shape of the base

Question 17

Which formula can be used to find the volume of a cone?

Accepted Answer

V = (1/3)πr²h

Answer

V = 4/3πr³

Answer

V = πr²h

Answer

V = (1/2)πr²h

Question 18

To derive the formula for the volume of a cone, which process is employed?

Accepted Answer

Dividing the cone into countless triangular prisms

Answer

Rotating a triangle around its axis of symmetry

Answer

Calculating the area of the cone's base and multiplying it by its height

Question 19

Which formula calculates the volume of a sphere?

Accepted Answer

(4/3)πr³

Answer

πr²h

Answer

lwh

Answer

(1/3)πr²h

Question 20

Which of the following shapes has a volume of 288π cm³?

Accepted Answer

Sphere with radius 6 cm

Answer

Cone with radius 6 cm and height 12 cm

Answer

Cylinder with radius 3 cm and height 16 cm

Answer

Cube with side length 6 cm

Question 21

Which of the following formulas is NOT used to calculate the volume of a cone?

Accepted Answer

V = l x w x h

Answer

V = π x r² x h

Answer

V = 4/3 x π x r³

Answer

V = 1/3 x π x r² x h

Question 22

What is the lateral surface area of a cone with a base radius of 4 cm and a slant height of 7 cm?

Accepted Answer

56π cm²

Answer

28π cm²

Answer

112π cm²

Answer

224π cm²

Question 23

Which of the following is a unit of surface area?

Accepted Answer

square meter (m²)

Answer

cubic centimeter (cm³)

Answer

cubic meter (m³)

Answer

liter (L)

Question 24

What is the formula to calculate the volume of a cylinder?

Accepted Answer

V = πr²h

Answer

V = 4/3πr³

Answer

V = Bh

Answer

V = Lwh

Question 25

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

Accepted Answer

Cube

Answer

Sphere

Answer

Cylinder

Answer

Cone

Question 26

Given that the volume of a cone is 120π cm³, and its height is 15 cm, find the radius of the base.

Accepted Answer

8 cm

Answer

4 cm

Answer

12 cm

Answer

16 cm

Question 27

Which of the following is not a method for calculating the volume of an irregular object?

Accepted Answer

Guesstimation

Answer

Water displacement

Answer

Formula

Answer

Measurement

Question 28

Which shape has the largest volume for a given surface area?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 29

Recall the formula for the volume of a cone.

Accepted Answer

V = (1/3)πr²h

Answer

V = πr²h

Answer

V = (4/3)πr³

Answer

V = (2/3)πr³

Question 30

Distinguish between volume and surface area.

Accepted Answer

Volume is the space inside, while surface area is the outside.

Answer

Surface area is the space inside, while volume is the outside.

Answer

Volume and surface area are identical.

Answer

Volume is always greater than surface area.

Question 31

Calculate the radius of a sphere with a diameter of 10 cm.

Accepted Answer

5 cm

Answer

10 cm

Answer

15 cm

Answer

20 cm

Question 32

Which formula is used to find the volume of a sphere with radius r?

Accepted Answer

4/3 πr³

Answer

πr³

Answer

πr²

Answer

2/3 πr³

Question 33

A cone has a base radius of 6 cm and a height of 8 cm. What is its surface area?

Accepted Answer

113.1 square cm

Answer

56.5 square cm

Answer

72 square cm

Answer

144 square cm

Question 34

Which formula can be used to find the volume of a cylinder with base radius r and height h?

Accepted Answer

πr²h

Answer

πr³

Answer

4/3 πr³

Answer

1/3 πr²h

Question 35

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 cm³

Answer

15 cm³

Answer

60 cm³

Answer

10 cm³

Question 36

Determine the volume of a triangular prism with a base area of 15 square centimeters and a height of 10 centimeters.

Accepted Answer

150 cm³

Answer

300 cm³

Answer

75 cm³

Answer

100 cm³

Question 37

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

140 cm³

Answer

79 cm³

Question 38

A cylinder has a radius of 4 inches and a height of 10 inches. Calculate its volume. (Use π = 3.14)

Accepted Answer

502.4 cubic inches

Answer

251.2 cubic inches

Answer

125.6 cubic inches

Question 39

A swimming pool is in the shape of a rectangular prism with a length of 20 feet, a width of 15 feet, and a depth of 5 feet. How many cubic feet of water can the pool hold?

Accepted Answer

1500 cubic feet

Answer

750 cubic feet

Answer

300 cubic feet

Answer

700 cubic feet

Question 40

A cube has a volume of 512 cubic inches. Determine the length of one side of the cube.

Accepted Answer

8 inches

Answer

6 inches

Answer

9 inches

Answer

7 inches

Question 41

What is the volume of a cube with side length 5 cm?

Accepted Answer

125 cm³

Answer

62.5 cm³

Answer

25 cm³

Answer

50 cm³

Question 42

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

Accepted Answer

46 cm²

Answer

60 cm²

Answer

24 cm²

Answer

32 cm²

Question 43

Determine the surface area of a sphere with radius 5 cm.

Accepted Answer

314.16 cm²

Answer

628.32 cm²

Answer

157.08 cm²

Question 44

A rectangular prism has a square base with side length 6 cm and a height of 8 cm. What is its volume?

Accepted Answer

288 cm³

Answer

144 cm³

Answer

360 cm³

Question 45

A rectangular prism with a square base has a volume of 216 cm³. If the base side length is 6 cm, what is its height?

Accepted Answer

6 cm

Answer

3 cm

Answer

9 cm

Answer

12 cm