Question

the area of the shaded sector is 8π. what is the measure of ∠sot, which corresponds to the minor arc st? a 34° b 45° c 48° d 50°

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 $A$ is the area of the sector, $\theta$ is the central - angle measure in degrees, and $r$ is the radius of the circle. Here, $r = 8$ and $A=8\pi$.

Step2: Substitute values into formula

Substitute $A = 8\pi$ and $r = 8$ into the formula $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$. We get $8\pi=\frac{\theta}{360^{\circ}}\times\pi\times8^{2}$.

Step3: Simplify the equation

First, cancel out $\pi$ on both sides of the equation. The equation becomes $8=\frac{\theta}{360^{\circ}}\times64$. Then, we can rewrite it as $\frac{\theta}{360^{\circ}}=\frac{8}{64}=\frac{1}{8}$.

Step4: Solve for $\theta$

Cross - multiply to find $\theta$. $\theta=\frac{1}{8}\times360^{\circ}=45^{\circ}$.

Answer:

B. $45^{\circ}$