Three metallic solid cubes whose edges are 3 cm,

Given, edges of three solid cubes are 3 cm, 4 cm and 5 cm, respectively.

∴                    Volume of first cube = (3)3 = 27 cm3

                  Volume of second cube = (4)3 = 64 cm3

and                volume of third cube = (5)3 = 125 cm3

∴      Sum of volume of three cubes = (27 + 64 + 125) = 216 cm3

Let the edge of the resulting cube = R cm

Then, volume of the resulting cube, R3 =216 ⇒ R = 6cm