Master 3D Shapes: Volume and Surface Area Formulas and Applications

Question 1

Out of the following, which is NOT a formula for the volume of a cylinder?

Accepted Answer

4/3πr³

Answer

πr²h

Answer

2πrh

Answer

πd²h

Question 2

Determine the lateral surface area of a cone with a radius of 5 cm and a height of 10 cm.

Accepted Answer

100π cm²

Answer

50π cm²

Answer

150π cm²

Answer

200π cm²

Question 3

A cone-shaped party hat has a diameter of 30 centimeters and a height of 20 centimeters. Calculate the volume of the hat.

Accepted Answer

1257 cm³

Answer

2513 cm³

Answer

628 cm³

Question 4

Which of the following solids has the smallest volume?

Accepted Answer

A cone with base radius 2 cm and height 6 cm

Answer

A sphere with radius 3 cm

Answer

A cylinder with radius 4 cm and height 5 cm

Answer

A rectangular prism with length 5 cm, width 3 cm, and height 4 cm

Question 5

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

Accepted Answer

A = 200π cm²

Answer

A = 100π cm²

Answer

A = 300π cm²

Answer

A = 400π cm²

Question 6

Identify the formula for calculating the surface area of a sphere.

Accepted Answer

SA = 4πr²

Answer

SA = πr²

Answer

SA = 2πrl

Answer

SA = 1/3πr²h

Question 7

Calculate the surface area of a rectangular prism with a length of 10 cm, a width of 5 cm, and a height of 4 cm.

Accepted Answer

110 cm²

Answer

90 cm²

Answer

100 cm²

Answer

120 cm²

Question 8

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

Accepted Answer

(500/3)π cm³

Answer

(4/3)π cm³

Answer

500π cm³

Answer

1000π cm³

Question 9

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

Accepted Answer

SA = 2 * pi * r * h + 2 * pi * r^2

Answer

SA = 4 * pi * r^2

Answer

SA = pi * r^2 * h

Answer

SA = 2 * pi * r * (r + h)

Question 10

Which of the following shapes has the largest volume for a given surface area?

Accepted Answer

Sphere

Answer

Cube

Answer

Cylinder

Answer

Cone

Question 11

Which of the following solids has a lateral surface that is a curved surface?

Accepted Answer

Cylinder

Answer

Prism

Answer

Pyramid

Answer

Cube

Question 12

Which of the following is a property of a regular pyramid?

Accepted Answer

All lateral faces are congruent isosceles triangles.

Answer

The base is a rectangle.

Answer

The volume is always greater than the volume of a cone with the same base and height.

Answer

All edges have equal length.

Question 13

Which of the following solids is a polyhedron?

Accepted Answer

Cube

Answer

Sphere

Answer

Cylinder

Answer

Cone

Question 14

The base of a pyramid is a square with a side length of 6 cm. If the height of the pyramid is 10 cm, calculate its volume.

Accepted Answer

120 cm³

Answer

60 cm³

Answer

30 cm³

Answer

15 cm³

Question 15

What is the surface area of a rectangular prism with dimensions 4 centimeters by 5 centimeters by 6 centimeters?

Accepted Answer

120 square centimeters

Answer

90 square centimeters

Answer

150 square centimeters

Answer

180 square centimeters

Question 16

Which formula can be used to calculate the volume of a pyramid?

Accepted Answer

V = (1/3)B · h

Answer

V = πr²h

Answer

V = 4/3πr³

Answer

V = 2πr²h

Question 17

A rectangular prism has a volume of 24 cm³ and a height of 4 cm. If its width is 3 cm, calculate its length.

Accepted Answer

6 cm

Answer

2 cm

Answer

4 cm

Answer

8 cm

Question 18

What is the formula to calculate the volume of a rectangular prism?

Accepted Answer

V = lwh

Answer

V = (1/3)πr³

Answer

V = πr²h

Answer

V = 4/3πr³

Question 19

Which of the provided formulas is NOT used to calculate the surface area of a cone?

Accepted Answer

SA = 4πr²

Answer

SA = πr² + πrl

Answer

SA = 2πr² + 2πrl

Answer

SA = πr(r + l)

Question 20

Identify the shape that is NOT a polyhedron.

Accepted Answer

Sphere

Answer

Cube

Answer

Cone

Answer

Cylinder

Question 21

Calculate the volume of a cylinder with a radius of 3 cm and a height of 8 cm.

Accepted Answer

48π cm³

Answer

24π cm³

Answer

72π cm³

Answer

144π cm³

Question 22

Estimate the volume of a spherical tank with a diameter of 10 m.

Accepted Answer

1048 m³

Answer

524 m³

Answer

2096 m³

Answer

4192 m³

Question 23

Identify the shape of the cross-section of a cylinder cut perpendicular to its base.

Accepted Answer

Circle

Answer

Rectangle

Answer

Triangle

Answer

Square

Question 24

Find the volume of a cone with a base area of 25π square centimeters and a height of 12 centimeters.

Accepted Answer

100π cubic centimeters

Answer

50π cubic centimeters

Answer

150π cubic centimeters

Answer

200π cubic centimeters

Question 25

Which of the following shapes possesses a curved surface?

Accepted Answer

Cylinder

Answer

Cube

Answer

Pyramid

Answer

Prism

Question 26

Which shape lacks edges?

Accepted Answer

Sphere

Answer

Cone

Answer

Cylinder

Answer

Pyramid

Question 27

Which polyhedron has the highest number of faces?

Accepted Answer

Dodecahedron

Answer

Cube

Answer

Octahedron

Answer

Tetrahedron

Question 28

Which of the following is a 2-dimensional shape?

Accepted Answer

Triangle

Answer

Cube

Answer

Cylinder

Answer

Sphere

Question 29

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

Accepted Answer

V = lwh

Answer

V = πr²h

Answer

V = 4/3πr³

Answer

V = (1/3)πr²h

Question 30

What is the lateral surface area of a cylinder with a radius of 3 cm and a height of 5 cm?

Accepted Answer

2πrh

Answer

πr²h

Answer

4πr²

Answer

(1/2)πr²h

Question 31

A cone has a radius of 6 cm and a slant height of 10 cm. What is the total surface area of the cone?

Accepted Answer

240π cm²

Answer

120π cm²

Answer

360π cm²

Answer

720π cm²

Question 32

What is the volume of a sphere with a radius of 4 cm?

Accepted Answer

V = (4/3)πr³

Answer

V = πr²h

Answer

V = 2πrh

Answer

V = (1/3)πr²h

Question 33

What is the formula for calculating the volume of a sphere with radius 'r'?

Accepted Answer

(4/3)πr³

Answer

(2/3)πr²h

Answer

πr²h

Answer

πrl

Question 34

Which of the following is not a characteristic of a cylinder?

Accepted Answer

Has a rectangular base

Answer

Has two circular bases

Answer

Has a curved surface

Answer

Has parallel bases

Question 35

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

Accepted Answer

V = l × w × h

Answer

V = 2 × (l × w + l × h + w × h)

Answer

V = π × r² × h

Answer

V = 4/3 × π × r³

Question 36

What is the formula for the surface area of a sphere with radius r?

Accepted Answer

4πr²

Answer

2πr²

Answer

πr²

Answer

3πr²

Question 37

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

Accepted Answer

96 cm³

Answer

48 cm³

Answer

24 cm³

Answer

12 cm³

Question 38

Which of the following is NOT a property of spheres?

Accepted Answer

Can fit inside a cube

Answer

All points on the surface are equidistant from the center

Answer

Has no edges or vertices

Answer

Has a constant cross-sectional area

Question 39

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

Accepted Answer

96 cm³

Answer

106 cm³

Answer

116 cm³

Answer

86 cm³

Question 40

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

Accepted Answer

96 cm³

Answer

144 cm³

Answer

48 cm³

Answer

288 cm³

Question 41

A cone has a radius of 4 centimeters and a slant height of 5 centimeters. What is its lateral surface area?

Accepted Answer

62.83 cm² (approximately)

Answer

125.66 cm²

Answer

31.42 cm²

Answer

20π cm²

Question 42

A sphere has a radius of 3 centimeters. What is its volume?

Accepted Answer

113.04 cm³ (approximately)

Answer

56.52 cm³

Answer

282.60 cm³

Answer

36 cm³

Question 43

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

3 cm

Answer

10 cm

Answer

2 cm

Question 44

What is the surface area of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm?

Accepted Answer

74 cm²

Answer

34 cm²

Answer

54 cm²

Answer

114 cm²

Question 45

What is the volume of a cube with a side length of **a** centimeters?

Accepted Answer

**a³** cm³

Answer

**a/2** cm³

Answer

**a²** cm³

Answer

**a/4** cm³

Question 46

A rectangular prism has a length of **l** cm, a width of **w** cm, and a height of **h** cm. What is its volume?

Accepted Answer

**l * w * h** cm³

Answer

**(l * w)/h** cm³

Answer

**l + w + h** cm³

Question 47

A pyramid has a square base with side length **s** cm and a height of **h** cm. What is its volume?

Accepted Answer

**(s² * h)/3** cm³

Answer

**s * h** cm³

Answer

**(2 * s) * h** cm³

Answer

**(s² + h)/3** cm³

Question 48

A cone has a radius of **r** cm and a slant height of **l** cm. What is its lateral surface area?

Accepted Answer

**π * r * l** cm²

Answer

**π * r * h** cm²

Answer

**2 * π * r * h** cm²

Answer

**(π * r²) + (π * r * h)** cm²

Question 49

A sphere has a radius of **r** cm. What is its volume?

Accepted Answer

**(4/3) * π * r³** cm³

Answer

**π * r² * h** cm³

Answer

**(π * r²) + (2 * π * r * h)** cm³

Answer

**(π * r³) + (2 * π * r * h)** cm³

Question 50

A rectangular prism has a volume of **V** cm³ and a base area of **B** cm². What is its height?

Accepted Answer

**V/B** cm

Answer

**V - B** cm

Answer

**B/V** cm

Question 51

A pyramid has a square base with side length **s** cm and a volume of **V** cm³. What is its height?

Accepted Answer

**(3 * V)/(s²)** cm

Answer

**(V/3s²)** cm

Answer

**(V/s²)** cm

Answer

**(2 * V/s²)** cm

Question 52

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

Accepted Answer

**(A - 2πr²)/(2πr)** cm

Answer

**(A + 2πr²)/2πr** cm

Answer

**(πr²)/(A - 2πr²)** cm

Answer

**(2πr²)/A** cm

Question 53

A cone has a volume of **V** cm³ and a height of **h** cm. What is its radius?

Accepted Answer

**∛((3*V)/(π*h))** cm

Answer

**(V*h)/π** cm

Answer

**(π*h)/V** cm

Answer

**(V/(π*h²))** cm

Question 54

A sphere has a surface area of **A** cm². What is its diameter?

Accepted Answer

**√(A/π)** cm

Answer

**(πA)/4** cm

Answer

**A/π** cm