Find the area of a sector with a central angle of 5.38 rad in a circle of radius 2.7 mi.
A = 1/2 r^2 θ = 1/2 * 2.7^2 * 5.38 = 19.601 mi^2
To find the area of a sector, you can use the formula:
Area of Sector = (θ/2π) * π * r^2
Given:
Central angle (θ) = 5.38 rad
Radius (r) = 2.7 mi
Now, substitute the values into the formula and calculate the area.
Area of Sector = (5.38/2π) * π * (2.7)^2
First, let's simplify 5.38/2π:
5.38/2π ≈ 0.855
Now, substitute this value along with the radius into the formula:
Area of Sector ≈ 0.855 * π * (2.7)^2
Calculating the power:
(2.7)^2 = 7.29
Now substitute it back into the formula:
Area of Sector ≈ 0.855 * π * 7.29
Next, calculate the product:
0.855 * π * 7.29 ≈ 18.717
Therefore, the area of the sector is approximately 18.717 square miles.