Question

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

Answer 1

Answer:

Area = 25π

Step-by-step explanation:

The shaded region is the sector of the circle

Area of a sector is given by the formula:

`Area=(\theta)/(360)*\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=(\theta)/(360)*2\pi r \\ \\ 5\pi=(90)/(360)*2(\pi)(r) \\ \\ 5\pi=(\pi r)/(2) \\ \\ 10\pi=\pi r \\ \\ r=(10\pi)/(\pi) \\ \\ r=10 \end{gathered}`

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

`\begin{gathered} Area=(90)/(360)*\pi r^2 \\ \\ Area=(1)/(4)*\pi(10^2) \\ \\ Area=(100\pi)/(4) \\ \\ Area=25\pi \end{gathered}`