Question

The sector of a circle with a diameter of 8 feet has a central angle measure of 45°. What is the area of the sector?

A. π/2 ft²

B. π ft²

C. 2 π ft²

D. 8 π ft²

Answer 1

so, we know the diameter is 8, so that means its radius is half that, or 4.

`\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =45 \end{cases}\implies A=\cfrac{(45)\pi (4)^2}{360}\implies A=2\pi ~ft^2`