Question

A mettalic rectangular cuboid of dimension 4cm×6cm×8cm is melted and some more metal is added to make a cube the measure of whose side is an interger. What will be the minimum volume of metal to be added and what side is cube.

Answer 1

Let the volume of metal added is X.
Then Volume of cube = 4 × 6 × 8 + X
= 192 + X ___(1)

Cube root (192) = 5.768
Next integer is 6.
Therefore side of cube is 6 cm
Volume of cube = 6^3 = 216 ____(2)

Equating (1) and (2),
X = 216 - 192 = 24.
Minimum Volume of metal to be added is
24 cm3

Answer 2

24 cm is the answer of your question