Question

What is the area of the shaded sector?

Answer 1

Answer:

 = 72*pi  or approximately 226.08

Step-by-step explanation:

The area of the entire circle is

A = pi * r^2

where r = 24

A = pi * 24^2

A = pi *576

45 degrees is part of a 360 degree circle

45/360  =1/8

Multiply the area by 1/8  since it is 1/8 of the circle

1/8 A = 1/8 * 576pi

         = 72*pi

If we approximate pi

           = 226.08

Answer 2

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r=24\\ \theta =45 \end{cases}\implies A=\cfrac{(45)(\pi )(24)^2}{360}\implies A=72\pi$