Question

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Answer 1

We know that,

Volume of cube = a³, where a = side of cube

According to the question,

Side of first cube, a₁ = 3 cm

Side of second cube, a₂ = 4 cm

Side of third cube, a₃ = 5 cm

Let us assume that the side of cube recast from melting these cubes = a

We know that the total volume of the 3 cubes will be the same as the volume of the newly formed cube,

Volume of new cube = (volume of 1^st + 2^nd + 3^rd cube)

⇒ a³ = a₁³ + a₂³ + a₃³

⇒ a³ = (3)³ + (4)³ + (5)³

⇒ a³ = 27 + 64 + 125 = 216

⇒ a = 6 cm

Therefore, side of cube so formed is 6 cm.