Question

A metallic cuboid of dimensions 18,12,8 is metalled .find the minimum volume of molten metal which should be added to mould into a cube whose edge is x cm where x is an integer.

Answer 1

$volume \: \: of \: \: cuboid \\ = 18 \times 12 \times 8 = 1728 \\ \\ \sqrt[3]{1728} = 12 \: \: which \: is \: an \: integer \\ so \: minimum \: volume \: of \: molten \\ metal \: to \: be \: added = 0$