The volume of a shape is how much space it takes up. You might need to calculate the volume of a space or shape if, for example, you wanted to know how much soil to buy to fill a planting box or how much concrete you need to complete your patio.
You’ll need your area skills in order to calculate the volume of a shape. In fact, as you already know how to calculate the area of most shapes, you are one simple step away from being able to find the volume of most shapes too!
Example: Calculating volume 1
The cross section on this shape is the L shape on the front. In order to work out the area you’ll need to split it up into two rectangles as you practised in the previous part of this section.
Rectangle 1 = 7 × 4 = 28 cm2
Rectangle 2 = 5 × 2 = 10 cm2
Area of cross section = 28 + 10 = 38 cm2
Now you have the area of the cross section, multiply this by the length to calculate the volume.
V = 38 × 10 = 380 cm3
Example: Calculating volume 2
The last example to look at is a cylinder. The cross section of this shape is a circle. You’ll need to use the formula to find the area of a circle in the same way you did in the previous part of this section.
You can see that the circular cross section has a radius of 8 cm. To find the area of this circle, use the formula:
A = πr2
A = 3.142 × 8 × 8
A = 201.088 cm2
Now you have the area, multiply this by the length of the cylinder to calculate the volume.
V = 201.088 × 15 = 3016.32 cm3
Now try yourself in the activity below.
Activity 7: Calculating prism volume
Work out the volume of the 3D trapezium (trapezoidal prism) shown below.
Hint: Go back to the section on area and remind yourself of the formula to find the area of a trapezium.
The cross section is a trapezium so you will need the formula:
- A =
- A =
- A =
- A = 35 cm2
Now you have the area of the cross section, multiply it by the length of the prism to calculate the volume.
- V = 35 × 20 = 700 cm3
The final part of this session will look at scale drawings and plans. It will require your previous knowledge of ratio as scale drawings are really just another application of ratio.
In this section you have learned:
- that volume is the space inside a 3D shape or space
- how to find the volume of prisms such as cuboids, cylinders and triangular prisms.