Question

If the volumes of two cubes are in the ratio 27 : 1, the ratio of their edges is

Answer 1

Here is your solutions

Given

volumes of two cubes are in the ratio 27 : 1

To find ratio of their edges :-

let

Edges of cube is a and b

volume of cube [a] = a^3

volume of cube [b] = b^3

$\frac{a {}^{3} }{b {}^{3} } = \frac{27}{1} \\ \\ \frac{a {}^{} }{b} = \frac{3}{1}$

hence

The ratio of cube edges will be 3:1

hope it helps you .

Answer 2

Here is the answer

Given =>
Ratio of Volume of two cubes = 27 : 1

To find =>
Ratio of their edges = ?

Solution

Let the edge of first cube be 'x'.

Let the edge of second cube be 'y'.

We know that,

$\bf{Volume \: of \: cube} = a {}^{3}$

Thus,

$\bf{Volume \: of \: 1st \: cube = x {}^{3}}$

$\bf{Volume \: of \: 2nd \: cube = y {}^{3} }$

Thus,
Their ratio is 27 : 1

$\bf{ \therefore \frac{27}{1} = \frac{x {}^{3} }{y {}^{3} }}$

$\bf{ \therefore \frac{ \sqrt[3]{27} }{ \sqrt[3]{1} }} = \frac{ {x}^{} }{ {y} }$

$\bf{ \frac{3}{1} = \frac{x}{y} }$

Thus,

The ratio of their edges is 3 : 1.
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Thanks!