A circle has an area of $M \mathrm{~cm}^{2}$ and a circumference of $N \mathrm{~cm}$. If $\frac{M}{N}=20$, what is the radius of the circle, in $\mathrm{cm}$ ?
(A) 10
(B) 20
(C) 40
(D) $\frac{1}{10}$
(E) $\frac{1}{20}$
Suppose the radius of the circle is $r \mathrm{~cm}$.

Then the area $M$ is $\pi r^{2} \mathrm{~cm}^{2}$ and the circumference $N$ is $2 \pi r \mathrm{~cm}$.

Thus, $\frac{\pi r^{2}}{2 \pi r}=20$ or $\frac{r}{2}=20$ or $r=40$.

ANSWER: (C)

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