# 4.16.1 3D Shapes - Volume

#### What is volume?

• The volume of a 3D shape is a measure of how much 3-D space it takes up
• You need to be able to calculate the volumes of a number of common shapes

#### Volume – cuboids, prisms, and cylinders

1. To find the volume of a cuboid use the formula:

Volume of a cuboid = length × width × height • You will sometimes see the terms  ‘depth’ or ‘breadth’ instead of ‘width’
• Note that a cuboid is in fact a rectangular-based prism

2. To find the volume of a prism use the formula:

Volume of a prism = area of cross-section × length • Note that the cross-section can be any shape, so:
As long as you know its area and length, you can calculate the volume of the prism
Or if you know the volume and length of the prism, you can calculate the cross-section area

3. To calculate the volume of a cylinder with radius and height, use the formula:

Volume of a cylinder = πr2h • Note that a cylinder is in fact a circular-based prism: its cross-section is a circle with area πr2, and its length is h

#### Volume – pyramids, cones, & spheres

4. To calculate the volume of a pyramid with height h, use the formula:

Volume of a pyramid = 1/3 × area of base × h • Note that to use this formula the height  must be a line from the top of the pyramid that is perpendicular to the base

5. To calculate the volume of a cone with base radius  and height h, use the formula:

Volume of a cone = 1/3 πr2h • Note that a cone is in fact a circular-based pyramid: as with a pyramid, to use the cone volume formula the height  must be a line from the top of the cone that is perpendicular to the base

#### Exam Tip

The formula for volume of a sphere or volume of a cone will be given to you in an exam question if you need it.  You need to memorise the other volume formulas!

### Worked Example

Close Close