Question

Find the area of the sector with a central angle of 60° and a radius of 5 inches. Round to the nearest tenth. A) 5.2 in2 B) 10.5 in2 C) 13.1 in2 D) 26.2 in2

Answer 1

Set up a proportional ratio considering that the total area is πr^2 so:

a/(πr^2)=α°/360°

a=(απr^2)/360, since α=60° and r=5

a=(60π5^2)/360 in^2

a≈13.0899...

a≈13.1 in^2 (to nearest tenth of a square inch)

Answer 2

The answer is the option C

`13.1\ in^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

In this problem we have

`r=5\ in`

substitute

`A=\pi (5)^(2)=25\pi\ in^(2)`

`360\°` subtends the complete circle of area equal to
`25\pi\ in^(2)`

so by proportion

Find the area of the sector with a central angle of
`60\°`

`(25\pi)/(360)(\ in^(2))/(degrees)=(x)/(60)(\ in^(2))/(degrees) \\ \\x=25\pi *60/360\\ \\ x= 13.1\ in^(2)`