Question

The area of a sector of a circle with a central angle of 40° is 20ft^2. Find the radius of the circle. Do not round any intermediate computations. Round your answer to the nearest tenth.__ ft

Answer 1

In order to find the radius of the circle use the following formula for the area of a piece of circle with a given central angle:

`A=(\theta)/(360)\pi r^2`

in this case you have:

A = 20 ft²

θ = 40°

r = ?

first, solve for r in the given formula and then replace the value of A:

`\begin{gathered} r=\sqrt[]{(360)/(\theta\pi)A} \\ r=\sqrt[]{(360)/(40\pi)(20)}ft\approx7.6ft \end{gathered}`

Hence, the radius of th cricle is r = 7.6 ft