Question

find the area of this sector if ( r = 4 ) and ( \theta = \frac{pi}{12} ) radians.

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given \(r = 4\) and \(\theta=\frac{\pi}{12}\), we substitute these into the formula:

$$
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$$

Step3: Simplify the expression

$$ A=\frac{8\pi}{12}=\frac{2\pi}{3} $$

Answer:

\(\frac{2\pi}{3}\)