Chapter 11.6, Problem 9PSB

a.

To determine

To calculate: The area of sector ABC with radius as $12$ .

Answer to Problem 9PSB

The area of sector ABCis $24\pi$ .

Explanation of Solution

Given:

Circle with region ABC and radius as 12.

Measure of arcAC is ${60}^{\circ }$ .

Formula Used:

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

Calculation:

  

Area of sector ABC $=(\frac{60^o}{360^o})\pi {(12)}^2$

  $\begin{array}{l}=\frac{1}{6}*144\pi \\ =24\pi \end{array}$

b.

To determine

To calculate: The area of shaded sector PQR with radius as 12.

Answer to Problem 9PSB

The area of sectorPQR is $12\pi$ .

Explanation of Solution

Given:

Circle with shaded region PQR and radius as 12.

Measure of arcPR is ${30}^{\circ }$ .

Formula Used:

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

Calculation:

  

Area of sector PQR $=(\frac{30^o}{360^o})\pi {(12)}^2$

  $\begin{array}{l}=\frac{1}{12}*144\pi \\ =12\pi \end{array}$

c.

To determine

To find: The area of sector XYZwith inscribed angle of ${10}^{\circ }$ .

Answer to Problem 9PSB

The area of sectorXYZis $8\pi$ .

Explanation of Solution

Given:

Circle with region XYZ and inscribed angle of ${10}^{\circ }$ .

Formula Used:

  $Inscribedangle=\frac{1}{2}(measureofarc)$

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

Calculation:

  

Inscribed angle $=\frac{1}{2}(measureofarc)$

  ${10}^{\circ }=\frac{1}{2}(measureofarc)$

measure of arc $={20}^{\circ }$

Area of sector XYZ $=(\frac{20^o}{360^o})\pi {(12)}^2$

  $\begin{array}{l}=\frac{1}{18}*144\pi \\ =8\pi \end{array}$