Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single cube whose diagonal is $12 \sqrt{3}$ cm. The sides of the cubes are

3 cm, 4 cm, 5 cm

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6 cm, 8 cm, 10 cm

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9 cm, 12 cm, 15 cm

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None of these

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Solution

The correct option is B 6 cm, 8 cm, 10 cm
Let the length of side of a cube be 'a' (by cube) then
diagonal length $= \sqrt{3} a = 12 \sqrt{3} \Rightarrow a = 12$
Vol. of 3 small cube $=$ Vol. of bid cube
$\Rightarrow (3 x)^{3} + (4 x)^{3} + (5 x)^{3} = 12^{3} \Rightarrow x^{3} = \frac{1728}{216}$
$\Rightarrow x = 2 ∴ s i d e s l e n g t h a r e 6, 8, 10 c m$

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