given a central angle of 66 degrees find the area of a sector in a circle of radius 12.1 inches
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To find the area of a sector in a circle, you can follow these steps:
Step 1: Recall the formula for the area of a sector:
Area = (θ/360) * π * r^2
Where θ is the central angle in degrees, π (pi) is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.
Step 2: Calculate the area of the sector using the given central angle of 66 degrees and the radius of 12.1 inches.
Area = (66/360) * π * (12.1)^2
Step 3: Substitute the values into the formula and calculate the area:
Area = (66/360) * 3.14159 * (12.1)^2
Area ≈ 8.812 square inches (rounded to three decimal places)
Therefore, the area of the sector is approximately 8.812 square inches.
Area of a circle:
A=r^2*pi
Area of a sector:
As=r^2*pi*(66°/360°)
As=12.1^2*3.14159*0.18333
As=146.41*3.14159*0.18333
As=84.3245 in^2