Calculate the area of the sector shown in the image.

Question

ScanSolve AI Tutor · Accepted Answer

Assuming the question asks for the area of the sector shown in the image:

Identify the given values.
The radius of the sector is $r = 2.5 \text{ m}$ .
The central angle of the sector is $\theta = 220^\circ$ .
State the formula for the area of a sector.
The area $A$ of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by:
$A = \frac{\theta}{360^\circ} \pi r^2$
Substitute the given values into the formula.
$A = \frac{220^\circ}{360^\circ} \pi (2.5 \text{ m})^2$
Calculate the area.
First, simplify the fraction and square the radius:
$A = \frac{22}{36} \pi (6.25 \text{ m}^2)$ $A = \frac{11}{18} \pi (6.25 \text{ m}^2)$
Multiply the numerical values:
$A = \frac{11 \times 6.25}{18} \pi \text{ m}^2$ $A = \frac{68.75}{18} \pi \text{ m}^2$ $A \approx 3.8194 \pi \text{ m}^2$
Using $\pi \approx 3.14159$ :
$A \approx 3.8194 \times 3.14159 \text{ m}^2$ $A \approx 12.000 \text{ m}^2$
Rounding to two significant figures, consistent with the given radius:
$A \approx 12 \text{ m}^2$
The area of the sector is $\text{12 m}^2$ .

Answer