Question

A metal cube of edge $12$ $cm$ is melted and formed into three smaller cubes. If the edges of the smaller cubes are $6$ $cm$ and $8$ $cm$ . Find the edge of the third smaller cube ?

Answer 1

Let the edge of the other cube be 'a'.

Given, ${12}^3=b^3+8^3+a^3$ (volume remains the same)

$a^3={12}^3-6^3-8^3$

$a^3=1728-216-512$

$a^3=1000$

$a=10$

Edge of the cube = 10 cm.