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 $r$

Here, $\theta = 68^{\circ}$ and $r = 8$.

Step3: Substitute values into the formula

$A=\frac{68}{360}\times\pi\times8^{2}=\frac{68}{360}\times\pi\times64=\frac{68\times64\pi}{360}=\frac{4352\pi}{360}=\frac{544\pi}{45}\approx38.07$.

Answer:

$\frac{544\pi}{45}\approx38.07$