Question

the circle has center o. its radius is 7 m, and the central angle a measures 50°. what is the area of the shaded region? give the exact answer in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Recall the formula for the area of a sector

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 $r$ is the radius of the circle.

Step2: Substitute the given values

We are given that $r = 7$ m and $\theta=50^{\circ}$. Substituting these values into the formula, we get $A=\frac{50^{\circ}}{360^{\circ}}\times\pi\times(7)^{2}$.

Step3: Simplify the expression

First, simplify $\frac{50}{360}=\frac{5}{36}$. Then, $(7)^{2}=49$. So, $A = \frac{5}{36}\times49\pi=\frac{245\pi}{36}$ $m^{2}$.

Answer:

$\frac{245\pi}{36}$ $m^{2}$