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.