# A cylindrical vessel having diameter equal to its height

Question:

A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completely. Find the diameter of the cylindrical vessel.

Solution:

A cylindrical vessel whose height is equal to its diameter is given.

It is filled with water.

We know that the volume of a cylinder $=\pi r^{2} h$

In this particular case,

Height is equal to the diameter, that is $h=2 r$,

The volume of cylindrical vessel becomes $=2 \pi r^{3}$

The water from this vessel is transferred into two identical cylindrical vessels of

Diameter = 42 cm and, heightÂ h= 21 cm

Volume of each vessel $=\pi(21)^{2} \times 21$

We know that the sum of the volumes of the two identical vessels must be equal to the volume of the given cylindrical vessel.

$\Rightarrow 2 \pi r^{3}=2 \times\left(\pi(21)^{2} \times 21\right)$

$r^{3}=(21)^{3}$

Therefore, $r=21$

The diameter of the given cylinder is 42 cm