Master 3D Geometry: Enhance Your Mathematics Education Skills

Question 1

A prism has been cut in half parallel to its base. Which shape will the cross-section be?

Accepted Answer

Rectangle

Answer

Triangle

Answer

Circle

Answer

Ellipse

Question 2

A pyramid has a square base with side length 5 cm. If the height of the pyramid is 10 cm, what is its volume?

Accepted Answer

125 cm³

Answer

50 cm³

Answer

100 cm³

Answer

200 cm³

Question 3

Which of the following nets **cannot** be folded into a cube?

Accepted Answer

A triangle with lines drawn to connect the vertices

Answer

A square with lines drawn to connect the midpoints of each side

Answer

A rectangle with lines drawn to connect the midpoints of the longer sides

Answer

A circle with lines drawn to connect the points on the circle that are 120° apart

Question 4

A regular tetrahedron has edges of length 3 cm. What is the surface area of the tetrahedron?

Accepted Answer

24 cm²

Answer

12 cm²

Answer

18 cm²

Answer

36 cm²

Question 5

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

Accepted Answer

Cylinder

Answer

Cone

Answer

Sphere

Answer

Pyramid

Question 6

Which of the following is a regular polyhedron?

Accepted Answer

Dodecahedron

Answer

Rhombus

Answer

Trapezium

Answer

Cylinder

Question 7

In any polyhedron, what is the relationship between the number of edges (E), vertices (V), and faces (F) as expressed by Euler's formula?

Accepted Answer

E + V - F = 2

Answer

E = V + F

Answer

E - V = F

Question 8

Which property does NOT belong to a cube?

Accepted Answer

10 faces

Answer

6 square faces

Answer

8 vertices

Answer

12 edges

Question 9

Which 3D shape possesses the greatest number of edges?

Accepted Answer

Icosahedron

Answer

Tetrahedron

Answer

Cube

Answer

Octahedron

Question 10

Describe the shape formed by a cylinder's cross-section when cut parallel to its base.

Accepted Answer

Circle

Answer

Square

Answer

Triangle

Answer

Rectangle

Question 11

Identify the net that can be folded to form a triangular prism.

Accepted Answer

A square and two equilateral triangles

Answer

Two squares and a rectangle

Answer

Three squares

Answer

Two rectangles and a circle

Question 12

Which of the following shapes is NOT a face of a cube?

Accepted Answer

Pentagon

Answer

Square

Answer

Triangle

Answer

Rectangle

Question 13

What is the purpose of a net in relation to a 3D shape?

Accepted Answer

A two-dimensional pattern that can be folded into a 3D shape

Answer

A blueprint for constructing a 3D shape

Answer

A cross-section of a 3D shape

Answer

A diagram of the internal structure of a 3D shape

Question 14

What is the measure of the dihedral angle between two adjacent faces of a regular tetrahedron?

Accepted Answer

109.5 degrees

Answer

60 degrees

Answer

90 degrees

Answer

120 degrees

Question 15

Identify the property that does NOT apply to a cube:

Accepted Answer

It possesses 12 edges

Answer

Each face is a square

Answer

All angles are right angles

Answer

It possesses 8 vertices

Question 16

Classify the cube as a type of polyhedron:

Accepted Answer

Regular polyhedron

Answer

Triangular prism

Answer

Cylinder

Answer

Sphere

Question 17

How many edges does a cone have?

Accepted Answer

1

Answer

2

Answer

4

Question 18

Which of the following polyhedra has the greatest number of vertices?

Accepted Answer

Dodecahedron

Answer

Octahedron

Answer

Cube

Answer

Tetrahedron

Question 19

In a cylinder, what is the name of the line segment that joins the centers of the two circular faces?

Accepted Answer

Axis

Answer

Circumference

Answer

Diameter

Answer

Radius

Question 20

Which of the given polyhedra is classified as a prism?

Accepted Answer

Cube

Answer

Sphere

Answer

Pyramid

Answer

Cylinder

Question 21

Which property is shared among all regular polyhedra?

Accepted Answer

Congruent faces and congruent edges

Answer

Only congruent edges

Answer

Only congruent faces

Answer

None of the above

Question 22

Which of the following 3D shapes has the greatest number of vertices?

Accepted Answer

Cube

Answer

Cone

Answer

Triangular prism

Answer

Sphere

Question 23

A rectangular prism has a volume of 24 cubic units. Its length is 4 units and its height is 3 units. What is its width?

Accepted Answer

2 units

Answer

6 units

Answer

4 units

Answer

3 units

Question 24

Which of the following nets can be folded into a cube?

Accepted Answer

(Image of a net of a cube)

Answer

(Image of a net of a sphere)

Answer

(Image of a net of a triangular prism)

Answer

(Image of a net of a cone)

Question 25

A cone has a radius of 5 cm and a height of 12 cm. Calculate its volume.

Accepted Answer

(100π) cm³

Answer

(75π/3) cm³

Answer

(125π/3) cm³

Answer

(225π/3) cm³

Question 26

Which of the following statements accurately describes a regular tetrahedron?

Accepted Answer

All faces are equilateral triangles.

Answer

It has a rectangular base.

Answer

All edges are equal in length.

Answer

It has 6 vertices.

Question 27

What shape is formed when a plane intersects a sphere at its center?

Accepted Answer

Circle

Answer

Square

Answer

Triangle

Answer

Rectangle

Question 28

Which of the following is NOT a polyhedron?

Accepted Answer

Sphere

Answer

Tetrahedron

Answer

Octahedron

Answer

Cube

Question 29

A rectangular pyramid has a square base with a side length of 4 cm. The height of the pyramid is 5 cm. Calculate its surface area.

Accepted Answer

72 cm²

Answer

(112 + 40) cm²

Answer

(52 + 40) cm²

Answer

(82 + 40) cm²

Question 30

Which of the following 3D shapes exhibits rotational symmetry about multiple axes?

Accepted Answer

Sphere

Answer

Triangular prism

Answer

Cylinder

Answer

Cube

Question 31

What is the Euler characteristic of a tetrahedron?

Accepted Answer

2

Answer

8

Answer

6

Answer

4