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 k}

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

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Solution

The correct option is B $\frac{k}{\sqrt[3]{n}}$
Given, edge of the cube is $k$ .
Then, Volume of cube $= k^{3}$ .

Let $x$ be edge of small cube.
Then, Volume of small cube $= x^{3}$ .

Therefore,
$\Rightarrow k^{3} = n x^{3}$
$∴ x = \frac{k}{\sqrt[3]{n}}$ .

Hence, option $B$ is correct.

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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√nGiven, edge of the cube is k.Then, Volume of cube =k3.Let x be edge of small cube.Then, Volume of small cube =x3.Therefore,⇒k3=nx3∴x=k3√n.Hence, option B is correct.

A cube of edge ' $k$ ' is divided into 'n' equal cubes. Determine the edge of the new cube.

The correct option is B $\frac{k}{\sqrt[3]{n}}$
Given, edge of the cube is $k$ .
Then, Volume of cube $= k^{3}$ .

Let $x$ be edge of small cube.
Then, Volume of small cube $= x^{3}$ .

Therefore,
$\Rightarrow k^{3} = n x^{3}$
$∴ x = \frac{k}{\sqrt[3]{n}}$ .

Hence, option $B$ is correct.