Question

the diameter of a circle is 14 feet. what is the area of a sector bounded by a 54° arc?
54°
d=14 ft
give the exact answer in simplest form.
square feet
π
品
submit
work it out

Explanation:

Step1: Find the radius of the circle

The formula for radius \(r\) is \(r=\frac{d}{2}\). Given \(d = 14\) ft, so \(r=\frac{14}{2}=7\) ft.

Step2: Use the sector - area formula

The formula for the area of a sector is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta = 54^{\circ}\) and \(r = 7\) ft.
Substitute the values: \(A=\frac{54}{360}\times\pi\times(7)^{2}\).
Simplify \(\frac{54}{360}=\frac{3}{20}\), then \(A=\frac{3}{20}\times\pi\times49=\frac{147}{20}\pi\) square feet.

Answer:

\(\frac{147}{20}\pi\)