A cube of edge ‘4k’ is divided into ‘n’ equal cubes. Find the edge of the new cube.

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

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\sqrt[3]{n}

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\frac{4 k}{\sqrt[3]{n}}

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\sqrt{n k}

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Solution

The correct option is C $\frac{4 k}{\sqrt[3]{n}}$
$L e t, k_{s} be the edge of the new cube.$
Volume of the bigger cube = Sum of the volume of the smaller cubes formed
$\Rightarrow (4 k)^{3} = n \times (k_{s})^{3}$
$\Rightarrow 64 k^{3} = n k_{s}^{3}$
$\Rightarrow k_{s}^{3} = \frac{64 k^{3}}{n}$
$\Rightarrow k_{s} = \frac{4 k}{\sqrt[3]{n}}$
$∴$ Edge of the new cube, $k_{s} = \frac{4 k}{\sqrt[3]{n}}$

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A cube of edge ‘4k’ is divided into ‘n’ equal cubes. Find the edge of the new cube.

The correct option is C 4k3√nLet,ks be the edge of the new cube. Volume of the bigger cube = Sum of the volume of the smaller cubes formed ⇒(4k)3=n×(ks)3 ⇒64k3=nk3s ⇒k3s=64k3n ⇒ks=4k3√n ∴ Edge of the new cube, ks=4k3√n