Q2 of 44 Page 14

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube (Assume that there is no loss of metal during melting)

Let the edge of the third smaller cube be x cm.


Three small cubes are formed by melting the cube of edge 12 cm.


Edges of two small cubes are 6 cm and 8 cm.


Now, volume of a cube = (side)3


Volume of the big cube = sum of the volumes of the three small cubes


⇒ (12)3 = (6)3 + (8)3 + (x)


⇒ 1728 = 216 + 512 + x3


⇒ 1728 = 728 + x3


⇒ x3 = 1728 – 728


⇒ x3 = 1000


⇒ x = 10 cm


Therefore, the edge of the third cube is 10 cm


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