Question

The radius of a circle is 8 kilometers. What is the area of a sector bounded by a 144° arc?Give the exact answer in simplest form. ____ square kilometers. (pi, fraction,)

Answer 1

Given the Circle below with radius r,

$\text{Where r = 8km, }\phi=144^0\text{ and }\pi=\pi$

The formula for the area, A, of the sector is given below as,

$A=\frac{\phi}{360^0}\times\pi r^2$

Substituting for r and the ∅ into the formula above,

$\begin{gathered} A=\frac{144^0}{360^0}\times\pi\times8^2 \\ A=\frac{2}{5}\times\pi\times64=25\frac{3}{5}\pi km^2 \end{gathered}$

Hence, Area A of the sector is 25 3/5 km²