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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?

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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
+87334
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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
+7155
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$$\frac{\text{central angle of sector}}{\text{2pi radians}}=\frac{\text{area of sector}}{\text{area of circle}} \\~\\ \frac{5\pi /4}{2\pi}=\frac{\text{area of sector}}{\pi(8^2)} \\~\\ \frac{5}{8}=\frac{\text{area of sector}}{(3.14)(64)} \\~\\ \frac{5}{8}=\frac{\text{area of sector}}{200.96} \\~\\ \frac{5(200.96)}{8}=\text{area of sector} \\~\\ 125.6=\text{area of sector}$$

125.6 square feet

hectictar  Mar 22, 2017
edited by hectictar  Mar 22, 2017