Find the area of the segment of a circle of radious 21 cm and corresponding central angle 30
the answer is 630
As = 30/360 * Ac = 30/360 * 3.14*21^2 = 115.4 cm^2.
To find the area of the segment of a circle, we can use the formula:
Area = (θ/360) * π * r^2
Where:
- θ is the central angle in degrees
- π is a mathematical constant approximately equal to 3.14
- r is the radius of the circle
In this case, the central angle is given as 30 degrees, and the radius is given as 21 cm. Plugging these values into the formula, we get:
Area = (30/360) * π * (21 cm)^2
Now, let's calculate it step by step:
Step 1: Convert the central angle from degrees to radians.
Since the formula expects the central angle to be in radians, we need to convert 30 degrees to radians. To do so, we use the conversion factor (pi/180):
30 degrees * (π/180) = 0.5236 radians
Step 2: Calculate the area.
Area = (0.5236 radians/360) * π * (21 cm)^2
= (0.0087266) * π * (441 cm^2)
≈ 12.24 cm^2
Therefore, the area of the segment of a circle with a radius of 21 cm and a corresponding central angle of 30 degrees is approximately 12.24 cm^2.