Question

find the area of the sector. leave your answer in terms of pi.
(there is a diagram of a circle with a sector labeled 75° and radius 14 ft)
options:

• $\frac{245}{6}pi$
• $72pi$
• $49pi$
• $\frac{35}{12}pi$

Explanation:

Step1: Recall sector area formula

The formula for the area of a sector is $A = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle and $r$ is the radius.

Step2: Substitute given values

Here, $\theta = 75^\circ$, $r = 14$ ft. Substitute into the formula:
$A = \frac{75^\circ}{360^\circ} \times \pi \times (14)^2$

Step3: Simplify the expression

First calculate $14^2 = 196$, then simplify the fraction:
$A = \frac{5}{24} \times 196\pi = \frac{980}{24}\pi = \frac{245}{6}\pi$

Answer:

$\frac{245}{6}\pi$