Question

A cuboid of dimensions 40 cm × 10 cm × 20 cm is melted to form a cube. Find the length of the side of the cube formed.

• A. 25 units
• B. 30 units
• C. 20 units
• D. 10 units

Answer 1

The correct option is C 20 units

Volume of a cuboid $=lwh$

$\therefore$ Volume of the given cuboid
$=40\times 10\times 20$
$=8000\text{cu units}$

This cuboid is melted to form a cube. Thus, the volume of the cube formed is equal to the volume of the cuboid melted.

$\therefore$ Volume of the cube formed
= 8000 cu units

But
Volume of a cube = Side $\times$ Side $\times$ Side

$\therefore$ 8000 = Side $\times$ Side $\times$ Side

Substituting the options, we get:
10 $\times$ 10 $\times$ 10 = 1000 cu units ($X$)
30 $\times$ 30 $\times$ 30 = 27000 cu units ($X$)
25 $\times$ 25 $\times$ 25 = 15625 cu units ($X$)
20 $\times$ 20 $\times$ 20 = 8000 cu units ($✓$)

Thus, the length of the cube is 20 units.