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=(\phi)/(360^0)*\pi r^2`

Substituting for r and the ∅ into the formula above,

`\begin{gathered} A=(144^0)/(360^0)*\pi*8^2 \\ A=(2)/(5)*\pi*64=25(3)/(5)\pi km^2 \end{gathered}`

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