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

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

then substiute the parameters, we have

`\begin{gathered} \text{Area of sector=} \\ (270^0)/(360)*3.14*9^2 \\ \text{Then} \\ (3)/(4)*3.14*81 \end{gathered}`

Simplify the expression above, we have

`(3)/(4)*3.14*81=190.755ft^2`

Therefore

The Area of the sector is 190.76 ft²