Question

the sector of a circle with a 60 - millimeter radius has a central angle measure of 30°. what is the exact area of the sector in terms of π? enter your answer in the box. mm²

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given that \(r = 60\) mm and \(\theta=30^{\circ}\).
Substitute these values into the formula: \(A=\frac{30^{\circ}}{360^{\circ}}\times\pi\times(60)^{2}\).
First, simplify \(\frac{30^{\circ}}{360^{\circ}}=\frac{1}{12}\).
Then, \((60)^{2}=60\times60 = 3600\).
So, \(A=\frac{1}{12}\times\pi\times3600\).

Step3: Calculate the value of the area

\(A=\frac{3600\pi}{12}\).
Divide \(3600\) by \(12\): \(3600\div12 = 300\).

Answer:

\(300\pi\)