﻿ Unfolding three Dimensional Figures Worksheet | Problems & Solutions

Unfolding three Dimensional Figures Worksheet

Unfolding three Dimensional Figures Worksheet
• Page 1
1.
Find the number of triangles you would need in a net to make a triangular prism.
 a. 6 b. 2 c. 4 d. 3

Solution:

A triangular prism has two triangular bases and three rectangular faces.

So, the number of triangles in the net to form a triangular prism is 2.

2.
Pick a net you could use to make a cone of radius 3 inches.

 a. Net 1 b. Net 2 c. Net 3 d. None of the above

Solution:

The radius of the circular base is 3 inches.

The circumference of the circular base = 2πr.

= 2 x π x 3
[Substitute r = 3.]

= 6π
[Multiply 2 and 3.]

In nets (2) and (3), the length of the arc = 6π.

To form a cone, the circumference of the circle must equal the length of the arc and the circle should be adjacent to the arc.

In net (3), the length of the arc, 6π and the circumference of the circle, 4π are not equal.

So, only net (2) can be used to form a cone.

3.
Identify the solid that can be formed by the net.

 a. pyramid b. square pyramid c. triangular pyramid d. triangular prism

Solution:

A triangular pyramid will have four triangles of which, one is the base triangle and the other three triangles are the lateral faces. So, the above figure is a triangular pyramid.

A triangular prism has two triangular bases and three rectangular faces. So, the above figure cannot be a triangular prism.

A square pyramid has one square base and four triangular faces. So, the above figure is not a square pyramid.

A pyramid has triangular faces that meet at one point and a base that is a polygon. So, the above figure cannot be a pyramid.

When the above net is folded we get a triangular pyramid.

4.
Name the three dimensional figure that can be formed from the net.

 a. cube b. cone c. sphere d. cylinder

Solution:

A cylinder has two parallel, circular, and congruent bases.

A cone has one vertex and one circular base.

A cube has six square faces.

A sphere is the set of all points that are the same distance from a given point, called the center.

So, only a cylinder can be formed from the net.

5.
Which of the following figures represents a cone?

 a. Figure 2 b. Figure 4 c. Figure 3 d. Figure 1

Solution:

Since a cone has one vertex and one circular base, only Figure 4 represents a cone.

6.
Choose the figure which matches the following net.

 a. figure 1 b. figure 4 c. figure 3 d. figure 2

Solution:

Since, the net has three rectangular boxes and two triangles at the ends figure 2 can be drawn from the net.

So, figure 2 is the correct choice.

7.
Name the three dimensional figure that can be formed from the net.

 a. Triangular prism b. Cube c. Sphere d. Square pyramid

Solution:

The net has six equal squares.

The six equal squares form six square faces when folded.

A square pyramid has four triangular faces and a triangular prism has two triangular bases.

A cube has six congruent square faces.

So, only a cube can be formed from the net.

8.
Which of the nets can be folded to form a triangular pyramid?

 a. All the above b. Figure 3 c. Figure 1 d. Figure 2

Solution:

The net diagram of a triangular pyramid will have four triangles of which, one is the base triangle and the other three triangles are the lateral faces.

Among the figures, figure (3) has four triangles.

Figures (1) and (2) have squares in their nets, which are not required for a triangular pyramid.

So, only figure (3) can be folded to form a triangular pyramid.

9.
Which of the nets can be folded to form a triangular prism?

 a. Figure 3 b. Figure 1 c. All the above d. Figure 2

Solution:

A triangular prism has two triangular bases and three rectangular faces.

On folding figure 1, boxes 1 and 5 form the triangular faces and the boxes 2, 3, and 4 form the lateral faces.

So, figure 1 forms a triangular prism.

On folding figure 2, boxes 1 and 2 form the triangular faces and the boxes 3, 4, and 5 form the lateral faces.

So figure 2 forms a triangular prism.

On folding figure 3, boxes 1 and 2 form the triangular faces and the boxes 3, 4, and 5 form the lateral faces.

So, figure 3 forms a triangular prism.

All the figures form a triangular prism. So choice-D is the correct answer.

10.
What is the name of the three-dimensional figure which can be formed from the net in the figure?

 a. No three dimensional figure can be found b. Cone c. Triangular pyramid d. Cylinder

Solution:

The net diagram of the figure forms a three-dimensional figure with one circular base and one vertex.

The three-dimensional figure with one circular base and one vertex is called as cone.

So, a cone can be formed from the net in the figure.