Chapter 11, Problem 14RP

a.

To determine

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

Answer to Problem 14RP

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 $=\left(\frac{60^o}{360^o}\right)\pi {(12)}^2$

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

b.

To determine

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

Answer to Problem 14RP

The area of sectorPQR is $16\pi$ .

Explanation of Solution

Given:

Circle with sector PQR and radius as 12.

Measure of arcPR is ${40}^{\circ }$ .

Formula Used:

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

Calculation:

  

Area of sector PQR $=\left(\frac{40^o}{360^o}\right)\pi {(12)}^2$

  $\begin{array}{l}=\frac{1}{9}\times 144\pi \\ =16\pi \end{array}$

c.

To determine

To find: The area of sector XYZwith radius as $12$ .

Answer to Problem 14RP

The area of sectorXYZis $4\pi$ .

Explanation of Solution

Given:

Sector XYZ with radius as 12.

Measure of arc XZ as ${10}^{\circ }$ .

Formula Used:

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

Calculation:

  

Area of sector XYZ :

  $\begin{array}{l}=\left(\frac{10^o}{360^o}\right)\pi {(}^1\\ =\frac{1}{36}\times 144\pi \\ =4\pi \end{array}$