Question

the radius of a circle is 6 inches. what is the area of a sector bounded by a 115° arc?
115°
r=6 in
give the exact answer in simplest form.
square inches
π
品
submit
work it out

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given that \(\theta = 115^{\circ}\) and \(r = 6\) inches.
Substitute these values into the formula:
\(A=\frac{115}{360}\times\pi\times(6)^{2}\)

Step3: Simplify the expression

First, calculate \((6)^{2}=36\).
Then, \(\frac{115}{360}\times36=\frac{115\times36}{360}\).
Simplify \(\frac{115\times36}{360}=\frac{115}{10} = \frac{23}{2}\).

So, \(A=\frac{23}{2}\pi\)

Answer:

\(\frac{23}{2}\pi\) square inches