Question

The area of a sector of a circle with a central angle of 6pi/5 rad is 31 km2.

Find the radius of the circle.
r =
km

Answer 1

4.06 km

Explanation:

The area of the sector of a circle is given by the formula ...

A = 1/2r²θ

Filling in the given information, we have ...

31 km² = 1/2(r²)(6π/5)

Solving for r gives ...

r² = (31 km²)(5/(3π)) ≈ 16.446 km² . . . . divide by the coefficient of r²

r ≈ 4.055 km . . . . . . take the square root

The radius of the circle is about 4.06 km.