Volume

Volume is the amount of space that an object takes up.

Just as we can measure the area of a 2D (two dimensional) shape to find out how much space it takes up in two dimensions, we can measure the amount of space that a 3D object takes up in three dimensions. This is volume.

The simplest object to start with is a cube

A cube is a special sort or prism where all of the sides are squares. In the cube above, all of the sides have length of 1. Let’s say they are measured in cm.

The area of each of the six squares that make up the surface of the prism are $1cm \times 1cm = 1cm^2$

The volume of the cube is $1cm \times 1cm \times 1cm= 1cm^3$

What is the volume of a square prism with a cross section with sides of 2cm and a length of 3cm?

The area of the cross-section of the prism is $2cm \times 2cm = 4cm^2$

The volume of the prism is the area of the cross section multiplied by the length of the prism which is $4cm^2 \times 3cm = 12cm^3$ . This is twelve centimetres cubed.

The picture below shows the prism split up into 12 one centimetre cubes.

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