Question

A circle with area \blue{100\pi}100πstart color #6495ed, 100, pi, end color #6495ed has a sector with a central angle of \purple{\dfrac{2}{5}\pi} 5 2 ​ πstart color #9d38bd, start fraction, 2, divided by, 5, end fraction, pi, end color #9d38bd radians .

Answer 1

The area of the sector is
`20\pi\ units^2`

Explanation:

The complete question is

A circle with area 100π has a sector with a central angle of 2/5π radians.

What is the area of the sector?

we know that

The area of circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector with a central angle of 2/5π radians

`(100\pi)/(2\pi)=(x)/((2\pi/5))\\\\x=50((2\pi)/(5))\\\\x=20\pi\ units^2`