Question

A metallic cube with side $20$ cm is melted and formed into a cuboid with base $10$ cm by $40$ cm. What will be its height?

Answer 1

Length of metallic cube $s=20$ cm
$\therefore$ Volume $=s^3=20\times 20\times 20=8000$ cm${}^3$

Since this cube is being melted to form the cuboid, volume of the cuboid will be same as that of the cube.

For the cuboid, length $l=40$ cm, breadth $b=10$ cm and height $h=h$ cm
$\therefore$ volume of the cuboid $=l\times b\times h=10\times 40\times h=400\times h$ cm${}^3$

So, $8000=400\times h$
Dividing both sides by $400$,
$⟹$ Height of the cuboid $=\frac{8000}{400}=20$ cm.