Q. 94 - Precalculus Enhanced with Graphing Utilities

Question

Find the area of the sector of a circle of radius $3$centimeters formed by an angle of ${60}^{\circ }$. Round the answer to two decimal places. 

Step-by-Step Solution

Answer

The area of the sector is $4.71c{m}^2$

Step 1. Given information

A circle with radius $3$cm makes an area with the angle${60}^{\circ }$

Step 2. Used formulae

The area of a circle with radius $r$ and angle $\theta$ is $A=\frac{1}{2}{r}^2\theta$

Step 3. Calculation

${60}^{\circ }=60·\frac{\mathrm{\pi }}{180}=\frac{\mathrm{\pi }}{3}$ radians

For the given problem, we substitute and the area is obtained as $A=\frac{1}{2}·3^2·\frac{\mathrm{\pi }}{3}=\frac{3\mathrm{\pi }}{2}\approx 4.7124c{m}^2$