Watch out
Using diameter in πr²
Scottish National 5 Mathematics
National 5 Maths Arc length and sector area
Calculate arc lengths, sector areas and reverse circle measures.
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
- Write the fraction angle/360
- Use the calculator's π key, distinguish radius from diameter and keep the full value until the final rounding; arc length uses linear units and sector area uses square units.
- Read the command word, record the units or requested form, and make the final answer match it.
Explanation
Arc length and sector area is an assessed part of Scottish National 5 Mathematics in the geometry area. Calculate arc lengths, sector areas and reverse circle measures.
Write the fraction angle/360
Multiply by the full circumference or full circle area.
For a reverse problem, form an equation and isolate the unknown.
The interactive bank below mixes direct skills, reverse questions, interpretation and contextual reasoning rather than repeating one number pattern.
Key formulae and rules
- arc length = angle/360 × 2πr
- sector area = angle/360 x πr²
Check
An arc is a fraction of a circumference and a sector is the same fraction of a circle; check the units are length or area as appropriate.
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 calculator's π key, distinguish radius from diameter and keep the full value until the final rounding; arc length uses linear units and sector area uses square units.
Worked examples
Worked example 1
Arc length and sector area worked example
Find the arc length for radius 8 cm and angle 135°.
- Arc = × 2π x 8
- Simplify to .
Answer: 6π cm
Watch out
- Using diameter in πr²
- Forgetting the two radii when finding sector perimeter.