A sector of a circle has an area of 18π square units. If the central angle of the sector is 45 degrees, what is the radius of the circle?
Correct: C
The formula for the area of a sector (A_sector) is A_sector = (θ/360°) * πr^2, where θ is the central angle in degrees and r is the radius.
Given A_sector = 18π and θ = 45 degrees.
18π = (45/360) * πr^2
Simplify the fraction: 45/360 = 1/8
18π = (1/8) * πr^2
Divide both sides by π:
18 = (1/8) * r^2
Multiply both sides by 8:
r^2 = 18 * 8
r^2 = 144
Take the square root:
r = sqrt(144)
r = 12 units. (Radius must be positive).