Question

Two cylindrical jars contain the same amount of milk. If their diameters are in the ratio $3:4$ find the ratio of their heights.

Answer 1

Let $r$ and $R$ are the radii of the base of two cylindrical jars.

Let $h$ and $H$ are the height of the two cylindrical jars.

Now,

$\Rightarrow \frac{Diameterofthefirstjar}{Diameterofthesecondjar}=\frac{3}{4}$

$\Rightarrow \frac{2\pi r}{2\pi R}=\frac{3}{4}$

$\Rightarrow \frac{r}{R}=\frac{3}{4}$

Again,

$\Rightarrow \frac{Volumeofthefirstjar}{Volumeofthesecondjar}=1$ [ since same amount of mil contain ]

$\Rightarrow \frac{\pi r^{2}h}{\pi R^{2}H}=1$

$\Rightarrow \frac{r^{2}h}{R^{2}H}=1$

$\Rightarrow \left(\frac{r^2}{R^2}\right)\times \frac{h}{H}=1$

$\Rightarrow {\left(\frac{3}{4}\right)}^2\times \frac{h}{H}=1$

$\Rightarrow \frac{9}{16}\times \frac{h}{H}=1$

$\Rightarrow \frac{h}{H}=\frac{1}{\frac{9}{16}}$

$\Rightarrow \frac{h}{H}=\frac{16}{9}$

$\Rightarrow \frac{H}{h}=\frac{9}{16}$

$\Rightarrow H:h=9:16$

So, the ratio of their height is $9:16.$

Hence, the answer is $9:16.$