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Year 7 Interactive Maths - Second Edition


Volume of a Solid

3 layers of 2 rows of 6 cubes

If the rectangular box were filled with 1 cm cubes, there would be:

6 2 cubes in the bottom layer

As there are 3 layers,

Volume = 36 cubic centimetres

Now note that the area of the box's base is given by:

Area = 12 square centimetres

From the above discussion, we can derive a formula for the volume of a rectangular box as follows:

Volume = Area of the base  height


In general:

The volume, V, of a solid is given by

Volume = Ah

where A is the area of the base (or cross-section) of the solid and h is the height.


The volume of the following solids are often required to solve real world problems.

Cube

A cube of side-length l units has a volume of V cubic units given by

Volume of a cube is the side-length cubed


Cuboid

A cuboid with length l units, width w units and height h units has a volume of V cubic units given by

V = lwh


Example 2

Find the volume of a cube of side 10 cm.

Solution:
V = 1000

So, the volume of the cube is 1000 cubic centimetres

 

A cube of side-length 10 cm


Example 3

Find the volume of a brick 20 cm by 10 cm by 5 cm.

Solution:
V = 1000

So, the volume of the brick is 1000 cubic centimetres

A brick of length 20 cm, width 10 cm and height 5 cm
 
Key Terms

solid, volume formula, base, height, volume of a cube, volume of a cuboid


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