A circle has a radius of 8 ft. What is the area of the sector formed by a central angle measuring 5(pi symbol)/4 radians?

Use 3.14 for pi.

Guest Mar 22, 2017

#1**+2 **

The area, A, is given by :

A = (1/2)(r^2) (theta) so we have

A = (1/2) (8^2) (5 *3.14)/4 =

(1/8) (8^2) * 5 * 3.14 =

8 * 5 * (3.14) = 125.6 sq ft

CPhill
Mar 22, 2017

#2**+3 **

\(\frac{\text{central angle of sector}}{\text{2pi radians}}=\frac{\text{area of sector}}{\text{area of circle}} \\~\\ \frac{5\pi /4}{2\pi}=\frac{\text{area of sector}}{\pi(8^2)} \\~\\ \frac{5}{8}=\frac{\text{area of sector}}{(3.14)(64)} \\~\\ \frac{5}{8}=\frac{\text{area of sector}}{200.96} \\~\\ \frac{5(200.96)}{8}=\text{area of sector} \\~\\ 125.6=\text{area of sector}\)

125.6 square feet

hectictar
Mar 22, 2017