What is the ratio of the volumes of a cylinder,

Given that the diameter and the height of the cylinder, cone and sphere are the same.

The volume of cylinder, $v_{1}=\pi r_{1}^{2} h_{1}=\pi\left(\frac{\mathrm{d}}{2}\right)^{2} \mathrm{~d}$

The volume of cone, $v_{2}=\frac{1}{3} \pi r_{2}^{2} h_{2}=\frac{1}{3} \pi\left(\frac{\mathrm{d}}{2}\right)^{2} \mathrm{~d}$

And the volume of sphere, $v_{3}=\frac{4}{3} \pi r_{3}^{3}=\frac{4}{3} \pi\left(\frac{\mathrm{d}}{2}\right)^{3}$

Therefore,

The ratio of their volumes,

$v_{1}=v_{2}=v_{3}$

$\Rightarrow \pi\left(\frac{\mathrm{d}}{2}\right)^{2} \mathrm{~d}=\frac{1}{3} \pi\left(\frac{\mathrm{d}}{2}\right)^{2} \mathrm{~d}=\frac{4}{3} \pi\left(\frac{\mathrm{d}}{2}\right)^{3}$

$\Rightarrow 3: 1: 2$

Hence, the ratio is 3 : 1 : 2