Q. 93 - Precalculus Enhanced with Graphing Utilities

Question

Find the area of the sector of a circle of radius $4$ meters formed by an angle of ${45}^{°}$. Round the answer to two decimal places. 

Step-by-Step Solution

Answer

The area of the sector A of the circle is $6.28m^2$

Step 1. Given information

The circle has an area of $4$ meters and it forms an area with the angle ${45}^{\circ }$

Step 2. Used formulae

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

Step 3. Calculation

${45}^{\circ }=45·\frac{\mathrm{\pi }}{180}=\frac{\mathrm{\pi }}{4}$radians.

For the given problem, we substitute and the area is obtained as  $A=\frac{1}{2}·4^2·\frac{\mathrm{\pi }}{4}=2\mathrm{\pi }\approx 6.2832m^2$