2002 Pascal Problem 25

A student has two open-topped cylindrical containers. (The walls of the two containers are thin enough so that their width can be ignored.) The larger container has a height of 20 cm, a radius of 6 cm and contains water to a depth of 17 cm. The smaller container has a height of 18 cm, a radius of 5 cm and is empty. The student slowly lowers the smaller container into the larger container, as shown in the cross-section of the cylinders in Figure 1. As the smaller container is lowered, the water first overflows out of the larger container (Figure 2) and then eventually pours into the smaller container. When the smaller container is resting on the bottom of the larger container, the depth of the water in the smaller container will be closest to

\textbf{(A)}\ 2.82\ \text{cm}\quad \textbf{(B)}\ 2.84\ \text{cm}\quad \textbf{(C)}\ 2.86\ \text{cm}\quad \textbf{(D)}\ 2.88\ \text{cm}\quad \textbf{(E)}\ 2.90\ \text{cm}

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

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.