Question

The diagram shows a sector of a circle radius 10 cm.

Find the perimeter of the sector, giving your answer correct to 1 decimal place.

Answer 1

P ≈ 43.6 cm

Explanation:

the perimeter (P) is the sum of the 2 radii and the arc

arc length = circumference of circle × fraction of circle

= 2πr ×
`(135)/(360)`

= 2π × 10 × 0.375

= 20π × 0.375

≈ 23.6 cm ( to 1 decimal place )

Then

P = 23.6 + 10 + 10 = 43.6 cm