Question

A rectangular cuboidal piece of metal of dimensions 3cm×4cm×5cm is melted. Some more of the metal is added and the resulting metal is cast into a cube. The cube has integral measures for its sides. What is the minimum amount of metal that is added and what is the size of this cube ?

Answer 1

$volume \: \: of \: \: metal \: \: piece \\ = 3 \times 4 \times 5 = 60 \: {cm}^{3} \\ perfect \: \: cube \: \: near \: \: to \: \: and \: \: \\ higher \: \: than \: \: 60 \: \: is \: \: 64 \\ therefore \: \: extra \: \: metal \: \: to \: \: be \\ added \: \: is \: \: 4 \: {cm}^{3} \\ size \: \: of \: \: cube = \sqrt[3]{64} = 4 \: cm$