Question

if the volumes of two cubes are in the ratio 8:1 then the ratio of their edges is ​

Answer 1

Answer:

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Answer 2

Given:

Ratio of volumes of two cubes = 8 : 1

To find:

The ratio of their edges.

Solution:

Let x and y be the edges of two cubes

We know that volume of a cube is given by

(edge of the cube)³

So,

According to the question

$\implies \frac{ {x}^{3} }{ {y}^{3} } = \frac{8}{1 } \\ \\ = > {( \frac{x}{y}) }^{3} = \frac{8}{1}$

We know that 8 = (2)³

$\implies \: \left( \frac{x}{y} \right ) {}^{3} = \left( \frac{2}{1} \right) {}^{3} \\ \\ \: or \: it \: can \: also \: be \: written \: as \\ \implies \: \frac{x}{y} = \sqrt[3]{ \left( \frac{8}{1} \right)} \\ \\ \implies \: \frac{x}{y} = \frac{2}{1}$

Therefore,

x:y = 2:1

Hence, ratio of edges

=> 2:1