Question

find the area a of the sector shown in each figure. (a)

Explanation:

Step1: Recall sector - area formula

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 values of $\theta$ and $r$

From the figure, $r = 6$ and $\theta=73^{\circ}$.

Step3: Substitute values into the formula

$A=\frac{73}{360}\times\pi\times6^{2}$.
First, calculate $6^{2}=36$. Then $A=\frac{73}{360}\times\pi\times36$.
$A=\frac{73\times36\pi}{360}$.
Simplify the fraction: $\frac{73\times36\pi}{360}=\frac{73\pi}{10}=7.3\pi\approx7.3\times3.14 = 22.922$.

Answer:

$7.3\pi\approx22.922$