Question

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

Answer 1

SOLUTION :

Given :

The volumes of two cubes are in the ratio 27:1

To be found :

The ratio of their edges

 

As we know that,

Volume of cube = a³

[in which a is the edge of the cube]

So,

let volume of one cube be a³ (in which a is side/edge of the one cube) and

volume of second be b³ (in which b is the side/edge of second cube)

Now,

$\bf \frac{Volume\:\:of\:\:one\:\: cube}{Volume\:\:of\:\:second\:\:cube}=\frac{27}{1}\\\\\rightarrow \frac{a^{3}}{b^{3}}=\frac{27}{1}\\\\\rightarrow ({\frac{a}{b})}^{3}=\frac{27}{1}\\\\\rightarrow \frac{a}{b}=\sqrt[3]{\frac{27}{1}}\\\\ \rightarrow \frac{a}{b}=\frac{\sqrt[3]{27} }{\sqrt[3]{1} }\\\\\rightarrow \frac{a}{b}= \frac{3}{1}$

Hence,

The ratio of the edges of  the cubes is 3:1