3-cubes-of-metal-whose-edges-are-3-4-and-5-respectively-are-melted-and-formed-into-a-single-cube-If-there-be-no-loss-of-metal-in-the-process-find-the-side-of-the-new-cube-

Question Number 16419 by Mr easymsn last updated on 21/Jun/17

$$\mathrm{3}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{metal}\:\mathrm{whose}\:\mathrm{edges}\:\mathrm{are}\:\mathrm{3},\mathrm{4} \\ $$$$\mathrm{and}\:\mathrm{5}\:\mathrm{respectively}\:\mathrm{are}\:\mathrm{melted}\:\mathrm{and} \\ $$$$\mathrm{formed}\:\mathrm{into}\:\mathrm{a}\:\mathrm{single}\:\mathrm{cube}.\:\mathrm{If}\:\mathrm{there}\:\mathrm{be} \\ $$$$\mathrm{no}\:\mathrm{loss}\:\mathrm{of}\:\mathrm{metal}\:\mathrm{in}\:\mathrm{the}\:\mathrm{process}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{cube}. \\ $$

Answered by Tinkutara last updated on 22/Jun/17

$$\mathrm{Total}\:\mathrm{volume}\:=\:\mathrm{3}^{\mathrm{3}} \:+\:\mathrm{4}^{\mathrm{3}} \:+\:\mathrm{5}^{\mathrm{3}} \:=\:\mathrm{216}\:\mathrm{cm}^{\mathrm{3}} \\ $$$$\mathrm{Side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{cube}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{216}\:\mathrm{cm}^{\mathrm{3}} }\:=\:\mathrm{6}\:\mathrm{cm} \\ $$

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