To find the area of the green sector, we can use the formula for the area of a sector in a circle, which is given by:
Area of sector = (m∠/360) × π × r²
where:
- m∠ is the measure of the angle of the sector in degrees,
- π is approximately 3.14, and
- r is the radius of the circle.
In this case, the angle m∠APB is 6° and the radius of the circle is 10 inches. Let’s substitute these values into the formula:
Area of sector = (6/360) × π × (10)²
Calculating the radius squared:
(10)² = 100
Now, substituting this back into the formula:
Area of sector = (6/360) × π × 100
Next, we can simplify (6/360) to (1/60):
Area of sector = (1/60) × π × 100
Now multiplying:
Area of sector = (100/60) × π
Which simplifies to:
Area of sector ≈ (5/3) × π ≈ 5.24 square inches (using π ≈ 3.14)
Thus, the area of the green sector is approximately 5.24 square inches.