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 )