Question

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

Answer 1

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}`