Question

whats the area of a sector of a circle that has a diameter of 10 in. if the length of the arc is 10 in.?
a) 75 sq in.
b) 100 sq in.
c) 50 sq in.
d) 25 sq in.

Explanation:

Step1: Find the radius

Given diameter \(d = 10\) in, radius \(r=\frac{d}{2}=\frac{10}{2}=5\) in.

Step2: Use the sector - area formula

The formula for the area of a sector \(A=\frac{1}{2}r\times l\), where \(l\) is the arc - length. Here \(r = 5\) in and \(l=10\) in.
Substitute the values into the formula: \(A=\frac{1}{2}\times5\times10\).
Calculate \(\frac{1}{2}\times5\times10 = 25\).

Answer:

D. 25 sq in.