Question

the area of the sector of a circle with a radius of 8 centimeters is 125.6 square centimeters. the estimated value of $\pi$is 3.14 the measure of the angle of the sector is

Answer 1

Solution

Given

Radius = 8cm, area = 125.6 square centimeters, pie =3.14

angle =?

$\begin{gathered} \text{Area of a sector =}\frac{\Theta}{360}\times\pi r^2 \\ 125.6\text{=}\frac{\Theta}{360}\times3.14\times8^2 \\ \\ 125.6\text{=}\frac{\Theta}{360}\times3.14\times64 \\ 125.6\text{=}\frac{200.96\Theta}{360} \\ \text{cross multiply} \\ 360\times125.6\text{ =}200.96\Theta \\ \text{Divide both sides by 200.96} \\ \\ \Theta=\frac{45216}{200.96} \\ \Theta=225^0 \end{gathered}$