Solids Geometry: Properties, Volume, Surface Area, and Applications

Question 1

Which property is unique to liquids and gases, but not solids?

Accepted Answer

Easily compressed

Answer

Fixed volume and definite shape

Answer

Relatively high density

Question 2

Which property is unique to solids?

Accepted Answer

Particles are closely packed together

Answer

Indefinite shape and volume

Answer

Particles are loosely arranged

Answer

Can flow like liquids

Question 3

Which property is NOT a defining characteristic of solids?

Accepted Answer

Ability to flow

Answer

Fixed shape

Answer

Definite volume

Answer

High density

Question 4

Find the volume of a sphere with a radius of 4 centimeters (cm).

Accepted Answer

Approximately 268.08 cubic centimeters (cm³)

Answer

16π cubic centimeters (cm³)

Answer

64π cubic centimeters (cm³)

Question 5

Calculate the surface area of a sphere with a radius of 3 centimeters (cm).

Accepted Answer

Approximately 113.1 square centimeters (cm²)

Answer

108π square centimeters (cm²)

Answer

9π square centimeters (cm²)

Question 6

What is the surface area of a rectangular prism with a length of 6 centimeters (cm), a width of 4 centimeters (cm), and a height of 3 centimeters (cm)?

Accepted Answer

72 square centimeters (cm²)

Answer

108 square centimeters (cm²)

Answer

36 square centimeters (cm²)

Question 7

Find the volume of a sphere with a diameter of 8 centimeters (cm).

Accepted Answer

Approximately 2144.66 cubic centimeters (cm³)

Answer

256π cubic centimeters (cm³)

Answer

1024π cubic centimeters (cm³)

Question 8

Which property is NOT characteristic of solids?

Accepted Answer

Gases can easily flow

Answer

Solids are incompressible

Answer

Solids have a definite volume

Answer

Solids have a definite shape

Question 9

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

Accepted Answer

V = l x w x h

Answer

V = bh

Answer

V = πr²h

Answer

V = 4/3πr³

Question 10

Which of the following solids has the largest volume?

Accepted Answer

Sphere with radius 10 cm

Answer

Cylinder with radius 5 cm and height 10 cm

Answer

Cube with edge length 10 cm

Answer

Cone with radius 5 cm and height 10 cm

Question 11

What is the shape of the cross-section of a cylinder?

Accepted Answer

Circle

Answer

Rectangle

Answer

Square

Answer

Triangle

Question 12

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

Accepted Answer

A = 4πr²

Answer

A = πr²h

Answer

A = (1/3)πr²h

Answer

A = 2πr³

Question 13

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

Accepted Answer

30 cm³

Answer

10 cm³

Answer

60 cm³

Answer

15 cm³

Question 14

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

Accepted Answer

56 cm²

Answer

28 cm²

Answer

42 cm²

Answer

84 cm²

Question 15

Calculate the surface area of a sphere with radius 8 cm.

Accepted Answer

256π cm²

Answer

512π cm²

Answer

128π cm²

Answer

64π cm²

Question 16

Solids are characterized by specific properties. Which of the following is not a characteristic of solids?

Accepted Answer

Compressibility

Answer

Definite shape

Answer

Crystalline structure

Answer

Definite volume

Question 17

When dealing with the volume of cones, which formula should we use?

Accepted Answer

(1/3)πr²h

Answer

(1/2)πr²h

Answer

πr²h

Answer

(4/3)πr²h

Question 18

In the realm of solids, which shape boasts the largest volume?

Accepted Answer

Sphere

Answer

Cylinder

Answer

Cube

Answer

Cone

Question 19

What is the surface area of a sphere with a radius of 5 cm?

Accepted Answer

4πr² = 4π(5 cm)² = 100π cm²

Answer

2πr² = 2π(5 cm)² = 50π cm²

Answer

πr³ = π(5 cm)³ = 125π cm³

Answer

2πr³ = 2π(5 cm)³ = 250π cm³

Question 20

Which solid has a constant cross-sectional area and polygonal faces?

Accepted Answer

Prism

Answer

Cone

Answer

Cylinder

Answer

Sphere

Question 21

The volume of a pyramid is one-third the volume of a prism with the same base and height. True or False?

Accepted Answer

True

Answer

It depends on the shape of the base

Answer

False

Answer

It depends on the height of the solids

Question 22

The surface area of a cube is calculated as 6 times the square of its side length. What is the surface area of a cube with a side length of 4 cm?

Accepted Answer

96 cm²

Answer

48 cm²

Answer

24 cm²

Answer

12 cm²

Question 23

The surface area of a sphere is calculated as 4 times pi times the radius squared. What is the surface area of a sphere with a radius of 6 cm?

Accepted Answer

144π cm²

Answer

72π cm²

Answer

36π cm²

Answer

288π cm²

Question 24

The volume of a cube is calculated as the cube of its side length. What is the volume of a cube with an edge length of 8 cm?

Accepted Answer

512 cm³

Answer

128 cm³

Answer

64 cm³

Answer

256 cm³

Question 25

The volume of a cone is calculated as one-third times pi times the radius squared times the height. What is the volume of a cone with a radius of 4 cm and a height of 6 cm?

Accepted Answer

32π cm³

Answer

64π cm³

Answer

128π cm³

Answer

16π cm³

Question 26

Which of the following solids has the shape of a tetrahedron?

Accepted Answer

Regular pyramid with square base

Answer

Sphere

Answer

Rectangular prism

Answer

Cylinder

Question 27

Which of the following is not a property of a sphere?

Accepted Answer

Volume is 4/3 πr³

Answer

Symmetrical about its center

Answer

Has a circular cross-section

Answer

Surface area is 4πr²

Question 28

Which of the following solids is an example of a regular polyhedron?

Accepted Answer

Cube

Answer

Prism

Answer

Cone

Question 29

Which of the following statements about the surface area of a hemisphere is correct?

Accepted Answer

It is half the surface area of a sphere with the same radius.

Answer

It is equal to the surface area of a sphere with the same radius.

Answer

It is twice the surface area of a sphere with the same radius.

Question 30

Which of the following solids has an infinite number of faces?

Accepted Answer

Cylinder

Answer

Pyramid

Answer

Sphere

Answer

Prism

Question 31

Which of the following is NOT a property of solids?

Accepted Answer

They can be easily deformed.

Answer

They have a definite shape.

Answer

They have a definite volume.

Answer

They are made up of densely packed particles.

Question 32

A cylinder has a radius of 3 cm and a height of 6 cm. What is its lateral surface area?

Accepted Answer

36π cm²

Answer

144π cm²

Answer

72π cm²

Answer

18π cm²

Question 33

A cube has a side length of 4 cm. What is its total surface area?

Accepted Answer

96 cm²

Answer

48 cm²

Answer

192 cm²

Answer

384 cm²

Question 34

A sphere has a volume of 36π cm³. What is its radius?

Accepted Answer

3 cm

Answer

9 cm

Answer

12 cm

Answer

6 cm

Question 35

A cone has a radius of r cm and a height of h cm. What is its volume in terms of r and h?

Accepted Answer

(1/3)πr²h

Answer

πr²h

Answer

(2/3)πr²h

Answer

4/3πr²h