Find the area of the sector with diameter 24 feet central angle (15/16)pi

To find the area of the sector, we can use the formula for the area of a sector of a circle, which is (θ/2π) * πr², where θ is the central angle in radians, r is the radius of the circle, and π is a constant approximately equal to 3.14159.

Step 1: Convert the diameter to radius. The radius is half of the diameter, so r = 24/2 = 12 feet.

Step 2: Substitute the given values into the formula. The central angle is (15/16)π, so the formula becomes:

Area = ((15/16)π / 2π) * π * 12²

Step 3: Simplify the equation. The π in the numerator and denominator cancel out, leaving:

Area = (15/16 / 2) * 12²

Step 4: Calculate the area.

Area = (15/32) * 144 = 67.5 square feet.

So, the area of the sector is 67.5 square feet.