Question

Find the area of the shaded area express it as a fraction times pie

Answer 1

Answer:

Area = 25π

Explanation:

The shaded region is the sector of the circle

Area of a sector is given by the formula:

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

m

The length of the arc, PQ = 5π

Find the radius, using the formula for the length of an arc

$\begin{gathered} PQ=\frac{\theta}{360}\times2\pi r \\ \\ 5\pi=\frac{90}{360}\times2(\pi)(r) \\ \\ 5\pi=\frac{\pi r}{2} \\ \\ 10\pi=\pi r \\ \\ r=\frac{10\pi}{\pi} \\ \\ r=10 \end{gathered}$

Substitute r = 10, and θ = 90° into the formula:

$\begin{gathered} Area=\frac{90}{360}\times\pi r^2 \\ \\ Area=\frac{1}{4}\times\pi(10^2) \\ \\ Area=\frac{100\pi}{4} \\ \\ Area=25\pi \end{gathered}$