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The radius of a circle is 8 feet. What is the area of sector bounded by a 90° arc?

The radius of a circle is 8 feet. What is the area of sector bounded by a 90° arc-example-1
User Tim Jahn
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1 Answer

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Since 90 degree is 1/4 of a circle, the area will be 1/4 th area of the full circle.

The radius is given by, r = 8 ft, therefore, the area of the full circle is,


\begin{gathered} A=\pi* r^2 \\ A=3.14*8^2=200.96ft^2 \end{gathered}

Therefore, the area of the sector is,


A^(\prime)=(1)/(4)*200.96ft^2=50.24ft^2
\begin{gathered} A^(\prime)=(\theta)/(360)*\pi* r^2 \\ \text{ =}\frac{\text{90}}{360}*\pi*8^2 \\ \text{ =}(1)/(4)\pi*64=16\pi \end{gathered}

User Jeeby
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