Question

The radius of two right curcular cones are equal, but the volumed are 4π m³ and 9π m³ respectively. The ratio of the height will be

Answer 1

Let the heights be h1 and h2.

Let radius be r.

Volume =$\frac{1}{3}*\pi*r^2*h$

For the first cylinder:

Volume=$4\pi m^3$

$\implies \frac{1}{3}\pi*r^2*h1=4\pi*m^3$

$\implies r^2*h1=12m^3$.......................(1)

Similarly:

For the second cylinder:

Volume=$9\pi m^3$

$\implies \frac{1}{3}\pi*r^2*h2=9\pi*m^3$

$\implies r^2*h2=27m^3$.........................(2)

Dividing (1) amd (2) we get:-

$\frac{h1}{h2}=\frac{12}{27}$

$\implies {4}{9}$

Thats the ratio of heights.

Hope it helps.