A cylindrical vessel having diameter equal to its height

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, height 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