Question

find the area a of the sector of a circle of radius 60 miles formed by the central angle \\(\frac{1}{6}\\) radian.

a (area) = \\(\square\\) miles\\(^2\\)
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall sector area formula

The formula for the area \(A\) of a sector with radius \(r\) and central angle \(\theta\) (in radians) is \(A = \frac{1}{2}r^2\theta\).

Step2: Substitute given values

Here, \(r = 60\) miles and \(\theta = \frac{1}{6}\) radian. Substitute into the formula:
\[
A = \frac{1}{2} \times (60)^2 \times \frac{1}{6}
\]

Step3: Calculate step-by-step

First compute \(60^2 = 3600\):
\[
A = \frac{1}{2} \times 3600 \times \frac{1}{6}
\]
Then \(\frac{1}{2} \times 3600 = 1800\):
\[
A = 1800 \times \frac{1}{6}
\]
Finally, \(1800 \times \frac{1}{6} = 300\)

Answer:

300 miles²