Question

the circle shown to the left with area 36π has a sector with a central angle of 48°. what is the area of the sector? choose 1 answer: a $\frac{5}{24}pi$ b $\frac{1}{270}pi$ c $270pi$ d $\frac{24}{5}pi$

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle of the sector and $\pi r^{2}$ is the area of the whole circle. We are given that the area of the whole circle $A_{circle}=\pi r^{2}=36\pi$ and $\theta = 48^{\circ}$.

Step2: Calculate the area of the sector

Substitute the given values into the formula: $A=\frac{48^{\circ}}{360^{\circ}}\times36\pi$. First, simplify $\frac{48}{360}=\frac{4}{30}=\frac{2}{15}$. Then, $A=\frac{2}{15}\times36\pi=\frac{72\pi}{15}=\frac{24\pi}{5}$.

Answer:

D. $\frac{24}{5}\pi$