Watch out
Using diameter as radius.
Scottish National 5 Mathematics
National 5 Maths Volume of standard solids
Calculate and reverse the volume of spheres, cones and pyramids.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Identify the solid and copy the correct formula.
- Use the π key and bracket the complete formula; keep full accuracy until the final answer and use cubic units.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Volume of standard solids is an assessed part of Scottish National 5 Mathematics in the geometry area. Calculate and reverse the volume of spheres, cones and pyramids.
Identify the solid and copy the correct formula.
Substitute radius and perpendicular height with units.
For reverse questions, undo multiplication and powers in order.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- V = πr³
- V = πr² h
- V = x base area x perpendicular height
Check
Compare the answer with a nearby cuboid or cylinder estimate and include cubic units.
Exam tip
Mark the diagram with the values you use, show the formula and finish with the correct length, area or volume units.
Calculator tip
Use the π key and bracket the complete formula; keep full accuracy until the final answer and use cubic units.
Worked examples
Worked example 1
Volume of standard solids worked example
Find the volume of a cone with radius 3 cm and height 8 cm.
- V = πr² h
- V = π x 9 × 8
Answer: 24π cm³
Watch out
- Using diameter as radius.
- Omitting the factor for cones and pyramids