A rectangular cubical piece of metal of dimensions 2cm ×3cm×4cm is melted. some more of the metal is added and it is made into a cube. The cube has integral measures for it's sides .What is the minimum amount of metal that is added and what is the size of this cube.
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The cuboid of 3 cm x 4 cm x 5 cm when melted will yield 60 cc of metal.
By adding the least amount of metal, say 4 cm, you get 64 cc of metal which can be cast into a cube of 4 cm size.
However, if you remove 0.681 cc and cast a cube of the remaining 59.319 cm you get a cube of 3.9 cm size, which is not an integer.
So, the best is to add 4 cc of metal to get a cube of 4 cm, or integer in size.
Step-by-step explanation:
I hope this helps you
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