Question

the diameter of a circle is 6 inches. what is the area of a sector bounded by a 35° arc? give the exact answer in simplest form. square inches

Explanation:

Step1: Find the radius of the circle

The radius \(r\) of a circle is half of the diameter. Given \(d = 6\) inches, so \(r=\frac{d}{2}=\frac{6}{2}=3\) inches.

Step2: Use the sector - area formula

The formula for the area of a sector of a circle 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 \(\theta = 35^{\circ}\) and \(r = 3\) into the formula:

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Answer:

\(\frac{7\pi}{8}\)