A rectangle has length $8 \mathrm{~cm}$ and width $\pi \mathrm{cm}$. A semi-circle has the same area as the rectangle. What is its radius?
(A) $4 \sqrt{2} \mathrm{~cm}$
(B) $4 \mathrm{~cm}$
(C) $16 \mathrm{~cm}$
(D) $8 \mathrm{~cm}$
(E) $2 \mathrm{~cm}$
A rectangle with length $8 \mathrm{~cm}$ and width $\pi \mathrm{cm}$ has area $8 \pi \mathrm{cm}^{2}$.

Suppose that the radius of the semi-circle is $r \mathrm{~cm}$.

The area of a circle with radius $r \mathrm{~cm}$ is $\pi r^{2} \mathrm{~cm}^{2}$ and so the area of the semi-circle is $\frac{1}{2} \pi r^{2} \mathrm{~cm}^{2}$. Since the rectangle and the semi-circle have the same area, then $\frac{1}{2} \pi r^{2}=8 \pi$ and so $\pi r^{2}=16 \pi$ or $r^{2}=16$.

Since $r>0$, then $r=4$ and so the radius of the semi-circle is $4 \mathrm{~cm}$.

ANSwER: (B)