Mark the correct alternative of the following. A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ration.

When a solid cylinder is melted and recast into a cone of the same radius, their volumes remain equal. The volume of the cylinder is pi*r^2*h_cylinder and the volume of the cone is (1/3)*pi*r^2*h_cone. Equating the two volumes gives pi*r^2*h_cylinder = (1/3)*pi*r^2*h_cone, which simplifies to h_cone = 3*h_cylinder. Therefore, the ratio of the height of the cone to the height of the cylinder is 3:1. The correct result is 3:1.

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