The area of the sector is 20π.
<u>Step-by-step explanation:</u>
- 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.
<u>To convert radian to degree :</u>
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°
<u>To find the area of the sector :</u>
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.
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