Question

the radius of a circle is 3 kilometers. what is the area of a sector bounded by a 30° arc?
give the exact answer in simplest form.
square kilometers

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given that \(\theta = 30^{\circ}\) and \(r = 3\) km.

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Answer:

\(\frac{3\pi}{4}\) square kilometers