Question

A rectangular tank $30cm\times 20cm\times 12cm$ contains water to a depth of $6cm$. A metal cube of side $10cm$ is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in litre, that must be poured in the tank so that the metal cube is just submerged in the water.

• A. $1.1l$
• B. $2l$
• C. $1.7l$
• D. $1.9l$

Answer 1

The correct option is B $2l$

As the rectangular tank contains water to a depth of $6$ cm and metal cube has side $10$ cm, we need to raise the water by $4$ cm which is equal to the volume $=30\times 20\times 4$ cm${}^3$.

But when the block is submerged in the water, it will also displace some volume of the water and that volume $=10\times 10\times 4$ cm${}^3$.

Volume of water to be poured in the tank $30\times 20\times 4$ cm${}^3$$-10\times 10\times 4$ cm${}^3$$=2000$cm${}^3$

Now as $1$ cm${}^3=0.001$ litres, therefore,

$2000$cm${}^3=2000\times 0.001=2$ litres

Hence, volume of water that must be poured in the tank is $2$ litres.