Question

An arc of a circle is of length 7pie cm and the sector it bounds has an area of 28pie cm square. Find the radius of the circle.

Answer 1

the radius of the sector is 8cm

Answer 2

The radius of circle is given as 8 cm

1) Given length of arc is 7π cm.

Formula for length of arc is (2πr) *(θ/360)

Equating both the lengths (2πr) *(θ/360) = 7π

rθ = 1260                                         ----------------> (1)

2) Given area of sector is 28π cm²

Formula for area of sector is (πr²)*(θ/360)

Equating both the areas (πr²)*(θ/360) = 28π

r²θ = 10080                                     ----------------> (2)

3) Dividing the second equation by 1

r²θ/rθ = 10080/1260

r =  8

4) Substituting in the first equation

8θ = 1260

θ = 157.5