Question

what is the area of the shaded sector?
24π
45π
72π
576π

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle with radius \( r \) and central angle \( \theta \) (in degrees) is \( A=\frac{\theta}{360}\times\pi r^{2} \).

Step2: Identify the values of \( \theta \) and \( r \)

From the diagram, the radius \( r = 24 \) and the central angle \( \theta=45^{\circ} \).

Step3: Substitute the values into the formula

Substitute \( \theta = 45^{\circ} \) and \( r = 24 \) into the formula:
\[

$$\begin{align*} A&=\frac{45}{360}\times\pi\times(24)^{2}\\ &=\frac{1}{8}\times\pi\times576\\ & = 72\pi \end{align*}$$

\]

Answer:

\( 72\pi \) (corresponding to the option "72π")