Question #N59
A circle has a circumference of $10\pi$ units. What is the area of the circle, in square units?
A. 5\pi
B. 10\pi
C. 25\pi
D. 100\pi
Correct Answer is: C
The circumference of a circle is given by the formula $C = 2\pi r$, where $r$ is the radius. We're given that the circumference is $10\pi$, so we can solve for the radius: \begin{align*} 10\pi &= 2\pi r \\ 5 &= r \end{align*} The area of a circle is given by the formula $A = \pi r^2$. Substituting 5 for $r$, we get $A = \pi (5)^2 = 25\pi$.