Question

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm, respectively are melted and formed into a single cube. Find the edge of the new cube formed.

Answer 1

We have,

Edges of the cubes : a₁ = 6 cm, a2 = 8 cm and a3 = 10 cm

Let the edge of the new cube so formed `= a_1^3 + a_2^3 + a_3^3`

⇒ a3 = 6³ + 8³ + 10³

⇒ a³ = 216 + 512 + 1000

⇒ a³ = 1728

`⇒ a = root(3)(1728)`

∴ a = 12 cm

So, the edge of the new cube so formed is 12 cm.