Question

A conical vessel whose internal radius is $10$ cm and height $48$ cm is full of water.

If this water is poured into a cylindrical vessel with an internal radius $20$ cm the height of the water level rises in it is _________ .

• A. $2cm$
• B. $3cm$
• C. $4cm$
• D. $5cm$

Answer 1

The correct option is C $4cm$

$\Rightarrow$ Radius of conical vessel $\left(R\right)=10cm$

$\Rightarrow$ Height of conical vessel $\left(H\right)=48cm$

$\Rightarrow$ Radius of cylindrical vessel $\left(r\right)=20cm$

$\Rightarrow$ Height of cylindrical vessel is $hcm$.

$\Rightarrow$ Volume of conical vessel $=$ Volume of a cylindrical vessel.

$\Rightarrow$ $\frac{1}{3}\pi R^{2}H=\pi r^{2}h$

$\Rightarrow$ $\frac{1}{3}\times \pi \times (10{)}^2\times 48=\pi \times (20{)}^2\times h$

$\Rightarrow$ $10\times 10\times 16=20\times 20\times h$

$\Rightarrow$ $h=\frac{16\times 10\times 10}{20\times 20}$

$\therefore$ $h=4cm$

Hence, the height of the water level is $4cm$.