Answer:
A. 1.78cm².
B. 331.34 square meters.
Explanation:
The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:
Area of shaded region = (θ/360) * πr²
Where:
- θ is the central angle in degrees.
- r is the radius of the circle.
- π is the mathematical constant pi, approximately equal to 3.14.
A.
If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:
Area of shaded region = (51/360)*π*2² = 0.357π m²
≈ 1.78 square meters
Therefore, the area of the shaded region is approximately 1.78square meters.
Therefore, the area of the shaded region is 1.78cm².
B.
If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:
Area of shaded region = (243/360)*π*12.5² = 105.47π m²
≈ 105.47π square meters
Therefore, the area of the shaded region is approximately 331.34 square meters.