Question

8. Find the measure of a central angle of a circle if it's sector area is 5π square inches and the radius is 6 in.

Answer 1

Given, sector area, A=5π.

The radius of the circle, r=6 in.

The sector area can be expressed as,

`\begin{gathered} A=(1)/(2)r^2*\theta \\ \text{Here, }\theta\text{ is the central angle in radians.} \end{gathered}`

Put A=5π, r=6 in in the above equation to find the central angle.

`\begin{gathered} 5\pi=(1)/(2)*6^2*\theta \\ 5\pi=(1)/(2)*36*\theta \\ (5\pi*2)/(36)=\theta \\ (10\pi)/(36)=\theta \\ (5\pi)/(18)=\theta \end{gathered}`

Therefore, the central angle is equal to 5π/18.