Question

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

Answer 1

We have,

Cylindrical vessel Diameter $=d=42cm.$

Then,

$Radius=r=21cm.$

Height $h=21cm.$

We know that,

Volume of cylinder

$Volume\left(1\right)=\pi r^{2}h$

$=\pi \frac{d^2}{4}\times d$

$=\frac{\pi d^3}{4}$

Now, Dimension of smaller cylinder

$Volume=\pi r^{2}h$

$=\pi \frac{d^2}{4}h$

Now, According to given question,

$Volume\left(1\right)=2\times volume$

$\frac{\pi d^3}{4}=2\times \frac{(\pi \times 42\times 42\times 21)}{4}$

$d^3=42\times 42\times 42$

$d^3={42}^3$

$d-42cm.$

Hence, the diameter is 42 cm.

This is the answer.