Question

Find the area of the sector of a circle of radius 9 ft with a central angle of 270°. Round the solution to two decimal places.

Answer 1

SOLUTION

Write out the given parameters

$\begin{gathered} \text{radius, r=9ft} \\ \theta=270^0 \end{gathered}$

The area of a sector is given by the formua

$\text{Area of sector=}\frac{\theta}{360}\times\pi r^2$

then substiute the parameters, we have

$\begin{gathered} \text{Area of sector=} \\ \frac{270^0}{360}\times3.14\times9^2 \\ \text{Then} \\ \frac{3}{4}\times3.14\times81 \end{gathered}$

Simplify the expression above, we have

$\frac{3}{4}\times3.14\times81=190.755ft^2$

Therefore

The Area of the sector is 190.76 ft²