Two right circular cones have heights in the ratio 1:2, and the circumferences of their bases are in the ratio 3:4. What is the ratio of their volumes?

Explanation

Given the height ratio as 1:2 and the base circumference ratio as 3:4, the ratio of the radii is also 3:4. Since the volume of a cone is proportional to the square of the radius times the height, the volume ratio is (3^2 * 1) : (4^2 * 2) = 9 : 32.