Question

A circle has a sector with area 3/2pi and central angle of 60 what is the area of the circle?

Answer 1

`A = 9\pi`

Explanation:

The total area of the circle is determine by simple rule of three:

`A = (360^(\textdegree))/(60^(\textdegree)) \cdot \left((3)/(2)\pi\right)`

`A = 9\pi`

Answer 2

The area of the circle is
`9\pi \ units^(2)`

Explanation:

we know that

A circle has a sector with area
`3\pi/2` and central angle of 60 degrees

The area of a complete circle subtends a central angle of
`360\°`

so

using proportion

Find the area of the circle

`((3\pi/2))/(60) =(x)/(360)\\ \\x=(3\pi/2)*360/60\\ \\x=9\pi \ units^(2)`