a metallic cuboid of dimensions 4cm x 6cm x 8cm is melted and some more metal is added to make it a cube whose side is an integer. find the minimum volume of the metal added and what is the side of the cube.
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Dimensions of cuboid are 4cm X 6cm X 8cm . Volume of a cuboid = Length x Width Height So , volume of given cuboid = 4 x 6 x 8 = 192 cm3 It is given that the cuboid is converted to a cube . Volume of cube = ( Side ) 3 It is given that some minimum volume is added to cuboid to make cube whose side is an integer . If we have a look at the perfect cube integers , cube nearest to 192 is 216 . So , Minimum volume of metal to be added = 216 - 192 = 24 cm3 Also , Volume of cube = ( Side ) 3 216 = ( Side ) Side = 6 cm So , minimum volume of metal to be added is 24 cm ' and side of cube is 6 cm .
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