Question

The volume of cube is $729m^3$ . 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 = $(side{)}^{3}orsideofcube=\sqrt[3]{Volumeofcube}$

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

Therefore from above we have
 $Volumeofcube={\left(side\right)}^3$
 $\Rightarrow side=\sqrt[3]{Volumeofcube}$
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:
 $\begin{array}{cc}3& 729\\ 3& 243\\ 3& 81\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$
Using prime factors. We have
 $$\begin{gathered} Sideofcube=\sqrt[3]{\underset{}{\underbrace{3\times 3\times 3}}\times \underset{}{\underbrace{3\times 3\times 3}}} \\ Sideofcube=3\times 3 \\ Sideofcube=9 \end{gathered}$$
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.