Question

I need help to find the area of the sector with an exact reduced fraction. I will send the photo:)

Answer 1

The area of the sector will be 7.5pi cm^2

Here, we want to get the area of the sector

Firstly, we need the measure of the angle subtended at the center of the circle

Since the sector is smaller, the angle subtended at the center will be 360 degrees minus the angle of the larger sector

That will be;

$360-285\text{ = 75}$

Mathematically, the formula for the area of a sector is;

$\begin{gathered} \frac{\theta}{360}\times\pi\times r^2 \\ \theta\text{ = 75} \\ r\text{ = 6 cm} \\ \text{Area will be;} \\ \frac{75}{360}\times\pi\times6^2\text{ = 7.5}\pi cm^2 \end{gathered}$