Question

What is the angle measure of an arc bounding a sector with an area 10 pi square kilometers

Answer 1

We would have to use the area of the sector and the radius provided to get the angle subtended at the centre of the circle.

Thus, we have:

`\begin{gathered} A_(\sec tor)=(\theta)/(360)*\pi* r^2 \\ 10\pi=(\theta)/(360)*\pi*15^2 \\ 10\pi=(\theta)/(360)*\pi*15^2 \\ 10\pi=(\theta)/(360)*\pi*225 \\ \text{The }\pi\text{ cancels out each other, we have:} \\ 10=(\theta)/(360)*225 \\ \theta=(10*360)/(225) \\ \theta=16^0 \end{gathered}`

Hence, the angle measure is 16 degrees.