2001 Pascal Problem 24

A sealed bottle, which contains water, has been constructed by attaching a cylinder of radius 1 cm to a cylinder of radius 3 cm, as shown in Figure A. When the bottle is right side up, the height of the water inside is 20 cm, as shown in the cross-section of the bottle in Figure B. When the bottle is upside down, the height of the liquid is 28 cm, as shown in Figure C. What is the total height, in cm, of the bottle?

\textbf{(A)}\ 29\quad \textbf{(B)}\ 30\quad \textbf{(C)}\ 31\quad \textbf{(D)}\ 32\quad \textbf{(E)}\ 48

If there are no answer choices shown, enter a numerical answer.

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