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,

$\begin{gathered} A=\pi\times r^2 \\ A=3.14\times8^2=200.96ft^2 \end{gathered}$

Therefore, the area of the sector is,

$A^{\prime}=\frac{1}{4}\times200.96ft^2=50.24ft^2$$\begin{gathered} A^{\prime}=\frac{\theta}{360}\times\pi\times r^2 \\ \text{ =}\frac{\text{90}}{360}\times\pi\times8^2 \\ \text{ =}\frac{1}{4}\pi\times64=16\pi \end{gathered}$