The circumference of a circle is 5π in. What is the area, in square inches? Express your answer in terms of piπ.
The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.
In this case, the circumference is 5π in, so we have 5π = 2πr.
Dividing both sides of the equation by 2π, we find that the radius is r = 5/2 inches.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Substituting the value of the radius we found, we have A = π(5/2)^2.
Squaring 5/2, we find that A = π(25/4).
The area of the circle is thus 25π/4 square inches.