The Diameter of a circle is 15in and has a nonshaded angle of 148*
13. Find the area of the shaded sector.
72.6 in^2
104.1 in^2
290.6 in^2
416.3 in^2
To find the area of the shaded sector, we need to first find the radius of the circle since the diameter is given.
Radius = Diameter / 2
Radius = 15 in / 2 = 7.5 in
Next, we find the area of the entire circle:
Area of circle = πr^2
Area of circle = π(7.5 in)^2
Area of circle = π(56.25) in^2
Area of circle ≈ 176.71 in^2
To find the area of the shaded sector, we use the formula for the area of a sector of a circle:
Area of sector = (θ/360) * Area of circle
Area of sector = (148/360) * 176.71 in^2
Area of sector ≈ 72.6 in^2
Therefore, the area of the shaded sector is 72.6 in^2, which means the correct answer is 72.6 in^2.