A circle has an arc length of 5π in. The central angle for this arc measures π/3 radians. What is the area of the associated sector?

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117.81 in²

Step-by-step explanation:

Given that,

arc length of sector = 5π

arc angle of sector = π/3

Formula to find the area of a sector of a circle

½ r² ∅

where

r is the radius

∅ the angle in radians subtended by the arc at the centre of the circle

First we need to find the radius of circle

length of arc = radius x angle of sector

5π = r x π/3

5π / (π/3) = r

r = 15

Now put this value in the formula of area of sector

½ (15) ² (π/3)

= 75π/2

= 117.81 in²