Master Solid Geometry: Conquer 3D Shapes in Mathematics

Question 1

Which of the following shapes fits the definition of a polyhedron?

Accepted Answer

Cube

Answer

Sphere

Answer

Cone

Answer

Cylinder

Question 2

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

Accepted Answer

Its surface consists of two circular faces

Answer

All points on its surface are an equal distance from the center

Answer

It is a three-dimensional shape

Answer

Its volume can be calculated as (4/3)πr³

Question 3

Which property is NOT exhibited by prisms?

Accepted Answer

Curved surfaces

Answer

Flat ends

Answer

Parallel sides

Answer

Equal base areas

Question 4

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

150 cubic centimeters

Answer

15 cubic centimeters

Answer

250 cubic centimeters

Question 5

The surface area of a sphere with radius 'r' is:

Accepted Answer

4πr²

Answer

2πr²

Answer

πr²

Answer

8πr³

Question 6

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

Accepted Answer

(1/3)πr²h

Answer

πr²h

Answer

(1/2)πr²h

Answer

4/3 πr³

Question 7

The lateral surface area of a cylinder with radius 'r' and height 'h' is:

Accepted Answer

2πrh

Answer

πrh

Answer

4πr²

Answer

2πr + 2πh

Question 8

The slant height of a cone with base radius 'r' and height 'h' is:

Accepted Answer

√(r² + h²)

Answer

√(r² - h²)

Answer

r + h

Answer

r - h

Question 9

What is the formula for calculating the volume of a cone with a base radius 'r' and a height 'h'?

Accepted Answer

πr²h

Answer

πrh

Answer

2πr²h

Answer

4/3πr²h

Question 10

Which diagram represents the net of a square-based pyramid?

Accepted Answer

[Diagram with a square base and four triangles forming the sides]

Answer

[Diagram with a triangular base and three triangles forming the sides]

Answer

[Diagram with a circular base and a curved surface]

Answer

[Diagram with a rectangular base and two triangles forming the sides]

Question 11

What is the shape of the cross-section of a cylinder made by a plane perpendicular to its base?

Accepted Answer

Circle

Answer

Square

Answer

Rectangle

Answer

Triangle

Question 12

Which of the following solids is formed by rotating a rectangle about one of its sides?

Accepted Answer

Cylinder

Answer

Prism

Answer

Pyramid

Answer

Cone

Question 13

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

30 cm³

Answer

10 cm³

Answer

15 cm³

Answer

60 cm³

Question 14

Calculate the volume of a cone with a base radius of 3 cm and a height of 4 cm.

Accepted Answer

(6π) cm³

Answer

(4π) cm³

Answer

(12π) cm³

Answer

(24π) cm³

Question 15

Identify the net that can form a regular tetrahedron.

Accepted Answer

Three equilateral triangles

Answer

A square and two triangles

Answer

Three squares and a triangle

Answer

Four squares

Question 16

What is the surface area of a cube with side length 4 cm?

Accepted Answer

144 cm²

Answer

48 cm²

Answer

96 cm²

Answer

192 cm²

Question 17

Identify the regular polyhedron with 8 faces.

Accepted Answer

Octahedron

Answer

Tetrahedron

Answer

Cube

Answer

Dodecahedron

Question 18

Which net can be folded to form a cone?

Accepted Answer

A semicircle

Answer

A circle

Answer

A square

Answer

A rectangle

Question 19

Calculate the volume of a prism with a rectangular base of length 5 cm and width 3 cm, and a height of 4 cm.

Accepted Answer

60 cm³

Answer

20 cm³

Answer

40 cm³

Answer

80 cm³

Question 20

Which solid has a circular base and a single vertex?

Accepted Answer

Cone

Answer

Cylinder

Answer

Sphere

Answer

Pyramid

Question 21

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

Accepted Answer

Circle

Answer

Rectangle

Answer

Triangle

Answer

Square

Question 22

Which of the following prisms has the largest base area?

Accepted Answer

Hexagonal prism

Answer

Square prism

Answer

Pentagonal prism

Answer

Triangular prism

Question 23

Determine 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

72 cm³

Answer

48 cm³

Answer

24 cm³

Question 24

Determine the volume of a cylinder with a base radius of 3 cm and a height of 6 cm.

Accepted Answer

54π cm³

Answer

36π cm³

Answer

72π cm³

Answer

18π cm³

Question 25

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

Accepted Answer

4πr²

Answer

πr³

Answer

2πrh

Answer

(1/3)πr²h

Question 26

A rectangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is its total surface area?

Accepted Answer

94 cm²

Answer

72 cm²

Answer

54 cm²

Question 27

Determine the volume of a pyramid with a square base of 6 cm side length and a height of 10 cm.

Accepted Answer

120 cm³

Answer

60 cm³

Answer

240 cm³

Question 28

Calculate the volume of a sphere with a diameter of 14 cm.

Accepted Answer

(14³)/6π cm³

Answer

(28³)/24π cm³

Answer

(7³)/3π cm³

Question 29

Calculate the surface area of a sphere with a radius of 4 cm.

Accepted Answer

64π cm²

Answer

16π cm²

Answer

32π cm²

Question 30

Find the lateral surface area of a cylinder with a radius of 3 cm and a height of 5 cm.

Accepted Answer

30π cm²

Answer

15π cm²

Answer

5π cm²

Answer

10π cm²

Question 31

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

Accepted Answer

(500/3)π cm³

Answer

(62.5/3)π cm³

Answer

(125/3)π cm³

Answer

(250/3)π cm³

Question 32

Find the volume of a sphere with a diameter of 12 cm.

Accepted Answer

288π cm³

Answer

36π cm³

Answer

216π cm³

Answer

864π cm³

Question 33

Calculate the length of one edge of a cube with a volume of 512 cm³.

Accepted Answer

8 cm

Answer

7 cm

Answer

6 cm

Answer

9 cm

Question 34

A metal sphere of radius 3 cm is melted down and recast into a cylinder with a radius of 4 cm. What is the height of the cylinder?

Accepted Answer

4.5 cm

Answer

3 cm

Answer

9 cm

Answer

6 cm

Question 35

Calculate the volume of a rectangular prism with length 8 cm, width 5 cm, and height 3 cm.

Accepted Answer

120 cm³

Answer

150 cm³

Answer

40 cm³

Answer

96 cm³

Question 36

Find the volume of a pyramid with a square base with side length 6 cm and a height of 4 cm.

Accepted Answer

48 cm³

Answer

72 cm³

Answer

36 cm³

Answer

144 cm³

Question 37

A cone has a radius of 5 cm and a height of 12 cm. What is its slant height?

Accepted Answer

13 cm

Answer

25 cm

Answer

17 cm

Answer

7 cm

Question 38

A sphere has a radius of 6 cm. What is its surface area?

Accepted Answer

144π cm²

Answer

36π cm²

Answer

288π cm²

Answer

144 cm²

Question 39

A cylinder has a diameter of 10 cm and a height of 15 cm. What is its total surface area?

Accepted Answer

550π cm²

Answer

750π cm²

Answer

300π cm²

Answer

450π cm²

Question 40

A cube has a volume of 64 cm³. What is the length of one of its sides?

Accepted Answer

4 cm

Answer

8 cm

Answer

16 cm

Answer

32 cm

Question 41

A cone has a radius of 4 cm and a height of 3 cm. What is its volume?

Accepted Answer

16π cm³

Answer

64π cm³

Answer

48π cm³

Answer

12π cm³

Question 42

A rectangular prism has a length of 12 cm, a width of 6 cm, and a height of 4 cm. What is its surface area?

Accepted Answer

288 cm²

Answer

144 cm²

Answer

576 cm²

Answer

360 cm²

Question 43

A pyramid has a square base with side length 8 cm and a height of 6 cm. What is its slant height?

Accepted Answer

10 cm

Answer

8 cm

Answer

16 cm

Answer

12 cm

Question 44

A sphere has a diameter of 14 cm. What is its volume?

Accepted Answer

1436.76π cm³

Answer

4116π cm³

Answer

343π cm³

Answer

1372π cm³