Chapter 11.6, Problem 10PSB

To determine

To calculate: The measure of arc ACwith area of sector ABCas $24\pi$ .

Answer to Problem 10PSB

The measure of arc ACis ${144}^{\circ }$ .

Explanation of Solution

Given:

Area of circle is $60\pi$ .

Area of sectorABC is $24\pi$ .

Formula Used:

Area of Sector $=\left(\frac{measureofarc}{360^o}\right)\pi r^2$ r = radius of circle.

Calculation:

  

Area of sector ABC $=\left(\frac{measureofarc}{360^o}\right)60\pi$

  $\begin{array}{l}24\pi =\frac{measureofarc}{360^o}*60\pi \\ \frac{24\pi }{60\pi }=\frac{measureofarc}{360^o}\\ \frac{2}{5}=\frac{measureofarc}{360^o}\\ 5*measureofarc=720^o\\ \therefore measureofarc=144^o\end{array}$