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 liters, that must be poured in the tank so that the metal cube is just submerged in water.

Answer 1

To solve this problem, we must make some assumptions:
1) The height of the tank is the $12cm$

2) The metal cube is already in the tank when the $6cm$ water depth is measured
to cover the cube with water we need another $4cm$ of water depth:
Height of cube $-$ height of water already in tank $=10-6=4cm$

Volume of cuboidal shape $=length\times breadth\times height,V=l\times b\times h$

The additional volume of water needed to cover the cube:
$V=30\times 20\times 4$

but the cube will displace some of that water, so we only need:
$V=30\times 20\times 4-10\times 10\times 4$
$=2000c{m}^3$
$=2000\times \left(\frac{1}{1000}\right)$ litre [$1$ litre $=1000c{m}^3$, $1c{m}^3=\frac{1}{1000}c{m}^3$]
$=2$ liters