A cube of edge ‘k’ is divided into ‘n’ equal cubes. Determine the edge of the new cube.

$\sqrt{n k}$

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$\frac{k}{\sqrt[3]{n}}$

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$\sqrt[3]{n}$

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$\frac{\sqrt[3]{n}}{k}$

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Solution

The correct option is B
$\frac{k}{\sqrt[3]{n}}$

In the given case, the volume is fixed as the larger cube is divided into 'n' smaller cubes.

Volume of the bigger cube = Sum of the volume of the smaller cubes formed
$k^{3} = n k_{s}^{3},$ where $k_{s}$ = edge of the new cube
$\Rightarrow k_{s} = \frac{k}{\sqrt[3]{n}}$
$∴$ Edge of the new cube, $k_{s} = \frac{k}{\sqrt[3]{n}}$

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A cube of edge ‘k’ is divided into ‘n’ equal cubes. Determine the edge of the new cube.

The correct option is B k3√n In the given case, the volume is fixed as the larger cube is divided into 'n' smaller cubes. Volume of the bigger cube = Sum of the volume of the smaller cubes formed k3=nk3s, where ks = edge of the new cube ⇒ks=k3√n ∴ Edge of the new cube, ks=k3√n