Question

The volume of cube is $ 729\,{m^3} $ . Length of its side in m.

Answer 1

Hint:For this we first let the side of a cube be ‘x’ and then form an equation using the mensuration volume formula of the cube and solving it to find the value of ‘x’ or required side of a cube.
Volume of a cube = $ {(side)^3}\,\,\,or\,\,\,side\,\,of\,\,cube = \sqrt[3]{{Volume\,\,of\,\,cube}} $

Complete step-by-step answer:
Let side of a cube = x m
Volume of given cube is = $ 729\,{m^3} $
But we know that the volume of a cube is given as $ {\left( {side} \right)^3} $ .

Therefore from above we have
 $ Volume\,\,of\,\,cube = {\left( {side} \right)^3} $
 $ \Rightarrow side = \sqrt[3]{{Volume\,\,of\,\,cube}} $
Substituting value of volume in above formula, we have,
To find the cube root of a number $ 729 $ we make its prime factors.
Prime factors of $ 729 $ are as follows:
 $ \begin{array}{*{20}{c}}
  3 & {729} \\
\hline
  3 & {243} \\
\hline
  3 & {81} \\
\hline
  3 & {27} \\
\hline
  3 & 9 \\
\hline
  3 & 3 \\
\hline
  {} & 1
\end{array} $
Using prime factors. We have
 $
 Side\,\,of\,\,cube = \sqrt[3]{{\underbrace {3 \times 3 \times 3}_{} \times \underbrace {3 \times 3 \times 3}_{}}} \\
  Side\,\,of\,\,cube = 3 \times 3 \\
  Side\,\,of\,\,cube\,\, = 9 \;
  $
Hence, from above we see that side a cube having volume $ 729 $ is $ 9 $ .

Note: Side of cube can be fide from given volume in two different way in first way we write given volume in term of exponent as $ {\left( 9 \right)^3} $ and then equating it with $ {(x)^3} $ to get value of x. And in other ways we find the cube root of a given volume by a prime factorisation method to find the value of the side of the cube as explained above.