Watch out
Using k for area or volume.
Scottish National 5 Mathematics
National 5 Maths Similarity
Use linked length, area and volume scale factors in forward and reverse problems.
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
- Match corresponding measures.
- Decide whether a calculator supports the method; exact working may still be required.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Similarity is an assessed part of Scottish National 5 Mathematics in the geometry area. Use linked length, area and volume scale factors in forward and reverse problems.
Match corresponding measures.
Find or identify the length scale factor k.
Square k for area or cube k for volume; take the matching root in reverse problems.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- length factor = k
- area factor = k²
- volume factor = k³
Check
Use k for lengths, k squared for areas and k cubed for volumes; the direction of the scale factor must match the question.
Exam tip
Mark the diagram with the values you use, show the formula and finish with the correct length, area or volume units.
Worked examples
Worked example 1
Similarity worked example
Similar solids have length scale factor 3. Find the volume scale factor.
- Volume uses the cube of the length factor.
- 3³ = 27
Answer: 27
Watch out
- Using k for area or volume.
- Comparing non-corresponding lengths.