Question : A metallic cube has sides of length 12 cm. It is melted and recast into three small cubes. Of these cubes, two have sides measuring 6 cm and 8 cm, respectively. The length of each side of the third cube is:
Option 1: 7 cm
Option 2: 9 cm
Option 3: 10 cm
Option 4: 5 cm
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Correct Answer: 10 cm
Solution :
A metallic cube has sides of length 12 cm.
So, its volume is $12^{3} = 1728$ cm
3
It is melted and recast into three small cubes.
Of these, two have sides measuring 6 cm and 8 cm, respectively.
Assume the side of the third cube is $x$.
So, $6^{3}+8^{3}+x^{3}=1728$
⇒ $216+512+x^{3}=1728$
⇒ $x^{3}=1728-728=1000$
⇒ $x=10$
Hence, the side of the third cube is 10 cm.
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