2023 Gauss 8 Problem 23

Each of two cylinders sits on one of their circular faces on a flat surface. Cylinder A, with radius 6 cm and height 50 cm, is empty. Cylinder B, with radius 8 cm and height 50 cm, is full of water. After pouring some water from Cylinder B into Cylinder A, the height of the water in both cylinders is the same. What is the height of the water? (The volume of a cylinder with radius r and height h is \pi r^2\ \text{h}.)

\textbf{(A)}\ 28.1 \text{ cm}\quad \textbf{(B)}\ 25.0 \text{ cm}\quad \textbf{(C)}\ 32.0 \text{ cm}\quad \textbf{(D)}\ 44.4 \text{ cm}\quad \textbf{(E)}\ 28.6 \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 Gauss contests here.