Question

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

Answer 1

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.