SOLID FIGURES AND NETS

A net is a 2-dimensional shape which can be folded to form a 3-dimensional shape or a solid figure.

Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.

A solid figure may have different nets.

Steps to Determine Whether a Net Forms a Solid Figure

1. Make sure that the solid and the net have the same number of faces.

2. The shapes of the faces of the solid have to match the shapes of the corresponding faces in the net.

3. We have to visualize how the net can be be folded to form the solid figure and also we have to make sure that all the sides fit together properly.

Net of a Cube

Let us find the net of the cube shown below.

In total, there are 11 possible nets for a cube as given below.

Net of a Cuboid

Let us find the net of the cuboid given below.

Here is the net of the cuboid given above.

Net of a Triangular Prism

Let us find the net of the triangular prism given below.

Here is the net of the triangular prism given above.

Net of a Pyramid

Let us find the net of the pyramid given below.

Here is the net of the pyramid prism given above.

Application of Net of a Solid Figure

One of the major applications of net is finding surface area of the solid figure.

For example, if we want to find surface area of a solid figure, then we have to get net of that solid figure and sum up the areas of all shapes we find in the net.

Practice Problem :

Find the surface area of the cuboid given below.

Here is the net of the cuboid given above.

Sum of the area of all shapes found in the net is

= 8x4 + 12x8 + 12x4 + 12x8 + 12x4 + 8x4

= 32 + 96 + 48 + 96 + 48 + 32

= 352 square cm

So, surface area of the cuboid is 352 square cm.

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