A fish tank, in the shape of a rectangular prism, has a base measuring $20 \mathrm{~cm}$ by $40 \mathrm{~cm}$ with a height of $30 \mathrm{~cm}$. The tank sits on a horizontal table and is half full of water. If $4000 \mathrm{~cm}^{3}$ of water is added, what is the new depth of the water?
(A) $5 \mathrm{~cm}$
(B) $15 \mathrm{~cm}$
(C) $20 \mathrm{~cm}$
(D) $25 \mathrm{~cm}$
(E) $10 \mathrm{~cm}$
Since the height of the fish tank is $30 \mathrm{~cm}$, and it is half full of water, then the depth of the water is $15 \mathrm{~cm}$.

Now the area of the base of the tank is $(20 \mathrm{~cm})(40 \mathrm{~cm})=800 \mathrm{~cm}^{2}$, and so $4000 \mathrm{~cm}^{3}$ of water will cover this base to a depth of $\frac{4000 \mathrm{~cm}^{3}}{800 \mathrm{~cm}^{2}}=5 \mathrm{~cm}$.

Therefore, the new depth of water is $15 \mathrm{~cm}+5 \mathrm{~cm}=20 \mathrm{~cm}$.

ANSWER: (C)