A cylinder with radius $2 \mathrm{~cm}$ and height $8 \mathrm{~cm}$ is full of water. A second cylinder of radius $4 \mathrm{~cm}$ and height $8 \mathrm{~cm}$ is empty. If all of the water is poured from the first cylinder into the second cylinder, the depth of the water in the second cylinder will be
(A) $1 \mathrm{~cm}$
(B) $2 \mathrm{~cm}$
(C) $3 \mathrm{~cm}$
(D) $4 \mathrm{~cm}$
(E) $6 \mathrm{~cm}$
The volume of a cylinder with radius $r$ and height $h$ is $\pi r^{2} h$.

When the cylinder with radius $2 \mathrm{~cm}$ and height $8 \mathrm{~cm}$ is full of water, it contains $\pi \times 2^{2} \times 8$ or $32 \pi \mathrm{cm}^{3}$ of water.

When this water is poured into the second cylinder, suppose it fills this second cylinder to a depth of $h$.

Then $32 \pi=\pi\left(4^{2}\right) h$ or $16 \pi h=32 \pi$ or $h=2 \mathrm{~cm}$.

Therefore, the depth of water in the second cylinder will be $2 \mathrm{~cm}$.

ANSWER: (B)