Question

A conical vessel whose internal radius is 10 cm and height 36 cm are full of water. The water is emptied into a cylindrical vessel with an internal radius of 20 cm. Find the height to which the water rises.

Answer 1

Given,

$r_1$ = radius of the conical vessel $=10cm$

$h_1$ = height of the conical vessel $=36cm$

$r_2$ = radius of the cylindrical vessel $=20cm$

Suppose water rises up to the height of $h_{2}cm$ in the cylindrical vessel.

Therefore,

Volume of water in conical vessel = Volume of water in cylindrical vessel

$\Rightarrow \frac{1}{3}\pi {r_1}^2{h}_1=\pi {r_2}^2{h}_2$

$\Rightarrow {r_1}^2{h}_1=3{r_2}^2{h}_2$

$\Rightarrow 10\times 10\times 36=3\times 20\times 20\times h_2$

$\Rightarrow h_2=3cm$

Hence, height of water rised in the cylindrical vessel is $3cm$.