A cylinder and a cone have equal radii of their bases and equal heights.
Question:

A cylinder and a cone have equal radii of their bases and equal heights. Show that their volumes are in the ratio 3:1.

Solution:

It’s given that

A cylinder and a cone are having equal radii of their bases and heights

Let the radius of the cone =radius of the cylinder = r

Height of the cone=height of the cylinder = h

Let the volume of cone = vx

Volume of cylinder = vy

$\Rightarrow \frac{v_{x}}{v_{y}}=\frac{\frac{1}{3} \pi r^{2} h}{\pi r^{2} h}=\frac{1}{3}$

⟹ vy/vx = 3/1

Therefore the ratio of their volumes is 3:1.