An arc of length 2 feet is cut off by a central angle of radians. Find the area of the sector formed. A)3.88 ft ² B)3.80 ft ² C)3.82 ft ² D)3.90 ft ² E)3.86 ft ²

Question

Quizplus · Accepted Answer

The area of a sector is given by the formula:

$A = \frac{1}{2}r^2	heta$

where $r$ is the radius and $	heta$ is the central angle in radians.

We are given that the length of the arc is 2 feet, which represents a fraction of the circumference of the circle:

$\frac{2}{2\pi r}=\frac{1}{\pi r}$

Simplifying, we get:

$r=\frac{2}{\pi}$

We are also given that the central angle is 11 radians.

Plugging in the values, we get:

$A = \frac{1}{2}\left(\frac{2}{\pi}ight)^2(11) \approx 3.82$

Therefore, the answer is (C) 3.82 ft.

An Arc of Length 2 Feet Is Cut Off by a Central