Question

The central angle of an arc measures 120° The radius of the circle measures 3 cm what is the area of the sector to the nearest hundredth of a square centimeter

Answer 1

The area of the sector should be 9.42
`cm^2` .

Explanation:

-The formula for finding the area of a sector:

`A = (Arc)/(360) \pi r^2`

-Next use the arc measure and the radius in order to solve and get the answer:

`A = (120\textdegree)/(360\textdegree)\pi 3^2`

-Solve:

`A = (120\textdegree)/(360\textdegree)\pi 3^2`

`A = (120\textdegree)/(360\textdegree)\pi *3^2`

`A = (1)/(3) \pi * 3^2`

`A = (1)/(3) \pi * 9`

`A = 3\pi \approx 9.424`

-Round to the nearest hundredth:

`A \approx 9.42`