Question

The area of a sector with a radius of 8 in. is 74.84 sq. in. Calculate theapproximate angle of the sector.The approximate central angle of the sector is [ang].

Answer 1

Given:

The area of a sector, A=74.84 sq. in.

The radius of the sector, r=8 in.

Now, the expression for the area of a sector can be written as,

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

Here, θ is the central angle in degrees.

Rearrange the above equation and substitute values to find the angle θ.

`\begin{gathered} \theta=(A)/(\pi r^2)*360^(\circ) \\ =141^(\circ) \end{gathered}`