Question

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.

Answer 1

Given details are,

Edge of metal cube (volume) = 12cm

Edge of smaller two cubes = 6cm, 8cm

Let edge of third cube be ‘a’ cm

So,

Volume of metal cube = sum of volume of three small cubes

123 = 63 + 83 + a3

1728 = 216 + 512 + a3

a3 = 1728 – 216 – 512

= 1000

a = 3√1000

= 10cm

∴ Edge of third smaller cube is 10 cm.