A circle with area 100 pie has a sector with a central angle of 2/5pi radius

The area of the sector is 20π.

Step-by-step explanation:

The area of the circle = 100π The formula for area of the circle = πr² The central angle of the sector = (2/5) π radians

The central angle should be converted from radians to degrees.

To convert radian to degree:

1 rad * 180/π gives the degree value.

Therefore, (2/5) π * 180/π = (2/5) * 180

The π gets cancelled out.

⇒ 2 * 36

⇒ 72°

To find the area of the sector:

The formula to calculate area of the sector = (central angle/360) * πr²

⇒ (72/360) * 100π

⇒ (1/5) * 100π

⇒ 20π

The area of the sector is 20π.