Final answer:
To find the area of a circle with a circumference of 15π inches, first determine the radius using the circumference formula, which is 7.5 inches, and then use the radius to calculate the area with the formula A = πr², resulting in an area of 56.25π square inches.
Step-by-step explanation:
The question asks to find the area of a circle knowing its circumference. The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius of the circle. First, we need to find the radius by using the given circumference 15π inches:
C = 2πr → 15π = 2πr
Dividing both sides by 2π, we find:
r = 7.5 in
Area of the circle is found using the formula A = πr². Substituting the radius we found, we get:
A = π(7.5)^2
A = π * 56.25
A = 56.25π square inches
Therefore, the area of the circle is 56.25π square inches.