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.

We know that,


Volume of cube = a3,


where a = side of cube


Now,


Side of first cube, a1 = 3 cm


Side of second cube, a2 = 4 cm


Side of third cube, a3 = 5 cm


Now, Let the side of cube recast from melting these cubes is 'a'.


As the volume remains same,


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


a3 = a13 + a23 + a33


a3 = (3)3 + (4)3 + (5)3


a3 = 27 + 64 + 125 = 216


a = 6 cm


So, side of cube so formed is 6 cm.


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