Question

this exercise involves the formula for the area of a circular sector. 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 circular sector 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, $r = 7$ and $\theta=60^{\circ}$.

Step3: Substitute values into formula

Substitute $r = 7$ and $\theta = 60$ into the formula: $A=\frac{60}{360}\times\pi\times7^{2}$.

Step4: Simplify the expression

First, $\frac{60}{360}=\frac{1}{6}$, and $7^{2}=49$. So $A=\frac{1}{6}\times\pi\times49=\frac{49\pi}{6}$.

Answer:

$\frac{49\pi}{6}$