Question

question 5
find the area of a sector of a circle with radius 14 inches subtended by a central angle of \\( \frac { 1 } { 2 } \pi \\) radians.
answer exactly in terms of pi.
\\( \square \\) square inches
question help: \\( \square \\) video \\( \square \\) written example \\( \square \\) message instructor
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Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 14\) inches and \(\theta=\frac{1}{2}\pi\) radians.
Substitute into \(A=\frac{1}{2}r^{2}\theta\):
\(A=\frac{1}{2}\times(14)^{2}\times\frac{1}{2}\pi\)
First, calculate \((14)^{2}=196\).
Then \(A=\frac{1}{2}\times196\times\frac{1}{2}\pi\)
\(\frac{1}{2}\times196 = 98\)
So \(A = 98\times\frac{1}{2}\pi\)
\(A = 49\pi\)

Answer:

\(49\pi\)