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.

Short answer

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

Step-by-step solution

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 asrole="math" localid="1646735777766" $A=\frac{1}{2}·4^2·\frac{\mathrm{\pi }}{4}=2\mathrm{\pi }\approx 6.2832m^2$