Vol of cylinder = \(\pi\)r\(^2\)H = vol of cone = \(\frac{1}{3}\)\(\pi\)r\(^2\)h H = height of cylinder and h = height of cone Let y = radius of cylinder = y, then radius of cone = 2y \(\pi\)y\(^2\)H = \(\frac{1}{3}\)\(\pi\)(2y)\(^2\)h y\(^2\)H = \(\frac{1}{3}\)4y\(^2\)h ( \(\pi\) cancels out and cross multiplying) The ratio of the height of the cylinder to that of the cone = \(\frac{\text{H}}{\text{h}}\) = \(\frac{4y^2}{3y^2}\) = \(\frac{4}{3}\) = 4: 3 (y\(^2\) cancels out )