Question

The radius of a circle is 9 miles. What is the area of a sector bounded by a 60° arc?Give the exact answer in simplest form. ____ square miles. (pi, fraction,)

Answer 1

Given a figure of a circle:

As shown, the radius of the circle = r = 9 miles

The shown sector bounded by a 60-degree arc

We need to find the area of the shown sector

as we know the area of the circle =

`\pi\cdot r^2`

The area of the sector represents 60/360 of the area of the circle

So, the area of the sector =

`(60)/(360)\cdot\pi\cdot r^2=(1)/(6)\cdot3.1416\cdot9^2=42.4115`

so, the answer will be the area of the shown sector = 42.4115 square miles

We will write the area in terms of pi and fractions as follow:

`(1)/(6)\cdot\pi\cdot9^2=(27)/(2)\pi`

So, the answer will be:

`(27)/(2)\pi`