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-

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

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

Answered by Tinkutara last updated on 22/Jun/17

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

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