Question

the diameter of a circle is 6 kilometers. what is the area of a sector bounded by a 54° arc?
54°
d=6 km
give the exact answer in simplest form.
square kilometers
π
submit
work it out

Explanation:

Step1: Find the radius of the circle

The formula for radius \(r\) is \(r=\frac{d}{2}\), where \(d\) is the diameter. Given \(d = 6\) km, so \(r=\frac{6}{2}=3\) km.

Step2: Use the sector - area formula

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.
Substitute \(\theta = 54^{\circ}\) and \(r = 3\) km into the formula:

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Answer:

\(\frac{27}{20}\pi\)