Question

In the diagram below, circle O has a radius of 10. If the measure of arc AB pointsis 72°, find the area of shaded sector AOB, in terms of tt. Show all yourwork that leads to the final answer.

Answer 1

Given:

Radius of the circle, r = 10

Measure of arc Ab, Θ = 72°

Let's find the area of the shaded sector.

To find the area of the shaded sector, apply the formula below:

$A_{\sec tor}=\frac{\theta}{360}\ast\pi r^2$

Substitute values into the formula:

$A_{\sec tor}=\frac{72}{360}\ast\pi\ast10^2$

Solving further, we have:

$\begin{gathered} A_{\sec tor}=0.2\ast\pi\ast100 \\ \\ A_{\sec tor}=0.2\ast100\ast\pi \\ \\ A_{\sec tor}=20\pi=62.83\text{ square units} \end{gathered}$

Therefore, the area of the shaded sector is 62.8 square units

ANSWER:

62.8 square units