Question

the radius of a circle is 1 foot. what is the area of a sector bounded by a 45° arc?
give the exact answer in simplest form.
square feet

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 \(\theta = 45^{\circ}\) and \(r = 1\) foot.
Substitute into the formula: \(A=\frac{45}{360}\times\pi\times(1)^{2}\).
Simplify \(\frac{45}{360}=\frac{1}{8}\).
So \(A=\frac{1}{8}\pi\) square feet.

Answer:

\(\frac{\pi}{8}\) square feet