Question

question
the circumference of a circle is 15π in. what is the area, in square inches? express your answer in terms of π.
answer attempt 1 out of 2
a = in² submit answer

Explanation:

Step1: Find the radius using the circumference formula

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=15\pi\), we have \(15\pi=2\pi r\). Dividing both sides by \(2\pi\), we get \(r=\frac{15}{2}\) inches.

Step2: Calculate the area using the radius

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = \frac{15}{2}\) into the formula, we have \(A=\pi(\frac{15}{2})^{2}=\pi\times\frac{225}{4}=\frac{225\pi}{4}\) square inches.

Answer:

\(\frac{225\pi}{4}\)