Question

find the area a of the sector of a circle of radius 40 meters formed by the central angle $\frac{1}{6}$ radian
a (area) $=\square$ meters $^{2}$
(type an integer or decimal rounded to three decimal places as needed.)

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given \( r = 40 \) meters and \( \theta=\frac{1}{6} \) radian.
Substitute into the formula: \( A=\frac{1}{2}\times(40)^{2}\times\frac{1}{6} \).
First, calculate \( (40)^{2}=1600 \).
Then, \( \frac{1}{2}\times1600\times\frac{1}{6}=\frac{1600}{12} \).
Simplify \( \frac{1600}{12}=\frac{400}{3}\approx133.333 \).

Answer:

\( 133.333 \)