1985 AIME Problem 2

When a right triangle is rotated about one leg, the volume of the cone produced is 800\pi \;\textrm{cm}^3. When the triangle is rotated about the other leg, the volume of the cone produced is 1920\pi \;\textrm{cm}^3. What is the length (in cm) of the hypotenuse of the triangle?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.