Question

this exercise involves the formula for the area of a circular sector. a sector of a circle has a central angle of 115°. find the area of the sector if the radius of the circle is 7 ft. (round your answer to one decimal place.) 48.8 × ft² resources

Explanation:

Step1: Convert angle to radians

First, convert $115^{\circ}$ to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, $115^{\circ}=115\times\frac{\pi}{180}=\frac{23\pi}{36}$ radians.

Step2: Use the sector - area formula

The formula for the area of a circular sector is $A = \frac{1}{2}r^{2}\theta$, where $r$ is the radius and $\theta$ is the central - angle in radians. Given $r = 7$ ft and $\theta=\frac{23\pi}{36}$ radians. Then $A=\frac{1}{2}\times7^{2}\times\frac{23\pi}{36}$.

Step3: Calculate the area

$A=\frac{1}{2}\times49\times\frac{23\pi}{36}=\frac{49\times23\pi}{72}$.
$A=\frac{1127\pi}{72}\approx49.7$ ft².

Answer:

$49.7$ ft²