Three cubes of sides $3$ cm, $4$ cm, and $5$ cm respectively are melted and recasted into a larger cube What is the side of the cube so formed?

12

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9

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8

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6

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Solution

The correct option is D $6$ cm
Given, $a_{1} = 3 c m$ , $a_{2} = 4 c m$ , and $a_{3} = 5 c m$ .

We know, the volume of a cube $V = a^{3}$ , where $a$ is the edge of the cube.

Volume of cube 1, $V_{1} = a_{1}^{3} = 3^{3} = 27 c m^{3}$ .
Volume of cube 2, $V_{2} = a_{2}^{3} = 4^{3} = 64 c m^{3}$ .
Volume of cube 3, $V_{3} = a_{3}^{3} = 5^{3} = 125 c m^{3}$ .
$∴$ Volume of the larger cube $V = V_{1} + V_{2} + V_{3}$
$= 27 + 64 + 125 = 216 c m^{3}$ .
Suppose $a$ is the required edge.
Then, $a^{3} = 216 c m^{3}$ .
$∴$ Edge of the larger cube $= \sqrt[3]{216} = 6 c m$

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