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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
avatar+87334 
+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

 

 

cool cool cool

CPhill  Mar 22, 2017
 #2
avatar+7155 
+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
edited by hectictar  Mar 22, 2017

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