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 completly. Find the diameter of the cylindrical vessel.

Answer 1

Let the height of the cylinder which is full of water initially be $h$.

So, its radius $=\frac{h}{2}$

and volume $=\pi {\left(\frac{h}{2}\right)}^2\times h=\frac{\pi h^3}{4}$

Now, volume of each smaller cylinder $=\pi \times \frac{42}{2}\times \frac{42}{2}\times 21=21\times 21\times 21\pi c{m}^3$

As per the question, $\frac{\pi h^3}{4}=2\times 21\times 21\times 21\pi$

$\Rightarrow h=2\times 21=42cm$

Hence, diameter = height = 42 cm