Question

(i) Calculate the arc length of a sector whose perimeter and radius are $35$ cm and $8$ cm respectively.
(ii) Find the radius of a sector whose perimeter and arc length are $24$ cm and $7$ cm respectively.

Answer 1

1. Perimeter of the sector $=2$(Radius) + Arc Length

Hence, Arc length $=Perimeter-2\times Radius=35-2\times 8=19cm$

2. Perimeter of the sector $=2$(Radius) + Arc Length

Hence, $2$ Radius $=Perimeter-Ar{c}^{\prime }sLength=24-7=17cm$

$Radius=8.5cm$