National 5MathsSQAApplications of MathematicsRevision NotesGeometric SkillsVolumeVolume of Standard Solids

Volume of Standard Solids (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Written by: Dan Finlay

Reviewed by: Roger B

Updated on 1 April 2026

Volume of prisms, cylinders, cones and spheres

How do I find the volume of a prism?

The formula for the volume of a prism is $V = A h$
- Multiply together the area of the cross-section and the height

Diagram of a 3D shape with highlighted cross-section and height. Formula V = A × h shown, where V is volume, A is area, h is height. — **Volume of a prism**

How do I find the volume of a cylinder?

The formula for the volume of a cylinder is $V = π r^{2} h$
- Square the radius
- Multiply by the height
- Multiply by π

Diagram of a cylinder with labels for radius and height, plus volume formula: V = π × r^2 × h, where r is radius and h is height. — **Volume of a cylinder**

How do I find the volume of a cone?

The formula for the volume of a cone is $V = \frac{1}{3} π r^{2} h$
- Square the radius
- Multiply by the height
- Multiply by π
- Divide by 3

Diagram of a cone with dashed lines showing height and radius. Formula for the volume is below: V = 1/3 × π × r² × h. — **Volume of a cone**

How do I find the volume of a sphere?

The formula for the volume of a sphere is $V = \frac{4}{3} π r^{3}$
- Cube the radius
- Multiply by π
- Multiply by $\frac{4}{3}$

Diagram of a sphere with a labelled radius; below is the volume formula: V = 4/3 × π × r³. — **Volume of a sphere**

Examiner Tips and Tricks

You are given all of these formulae in your exam. You do not need to memorise them. You just need to be able to use them.

Worked Example

A squash ball is a sphere with a diameter of 44 mm.

A simple grey circle with a black outline, measuring 44 mm in diameter.

Calculate the volume of the squash ball. Give your answer in cubic centimetres rounded to 1 decimal place.

Answer:

Divide the diameter by 10 to convert to centimetres

$44 mm = 4.4 cm$

Halve the diameter to find the radius

$4.4 cm \div 2 = 2.2 cm$

Use $V = \frac{4}{3} π r^{3}$

$\frac{4}{3} \times π \times 2 . 2^{3} = 44.60 . . .$

Round to 1 decimal place

44.6 cm³

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