Question

Two right circular cones X and Y are made X having 3 times the radius of Y and Y having half the volume of X. Calculate the ratio between the heights of X and Y.

Answer 1

Let radius of cone Y = r

Therefore, radius of cone X = 3r

Let volume of cone Y = V

Therefore, volume of cone X = 2V

Let h${}_1$ be the height of X and h${}_2$ be the height of Y.

Therefore,

Volume of cone X = $\frac{1}{3}\pi \left(3r^2\right)h_1$ = $3\pi r^2{h}_1$

Volume of cone Y = $\frac{1}{3}\pi r^2{h}_2$

Therefore,

$\frac{2V}{V}=\frac{9h_1}{h_2}$

$\frac{h_1}{h_2}=\frac{2}{9}$

$h_1:h_2=2:9$