A circle has a radius of 6 ft. Find the area of a sector if θ=150°
. Leave your answer in terms of π
.
The area of a sector of a circle is given by the formula A = (θ/360)πr^2, where θ is the central angle in degrees, r is the radius of the circle.
Given that the radius is 6 ft and θ = 150°, we can plug these values into the formula:
A = (150/360)π(6)^2
A = (5/12)π(36)
A = 15π
Therefore, the area of the sector with a central angle of 150° and a radius of 6 ft is 15π square feet.