A right circular cylinder and a right circular cone share the same radius and volume. What is the ratio of the cylinder's height to the cone's height?

Explanation

Given that both the cylinder and cone have identical radius and volume, the volume formulas are V_cylinder = πr²h_cylinder and V_cone = (1/3)πr²h_cone. Equating volumes, πr²h_cylinder = (1/3)πr²h_cone, which simplifies to h_cylinder = (1/3)h_cone. Therefore, the height ratio of cylinder to cone is 1:3.