Courses
Courses for Kids
Free study material
Offline Centres
More
Store

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

Last updated date: 06th Sep 2024
Total views: 422.4k
Views today: 5.22k
Verified
422.4k+ views
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 = ${(side)^3}\,\,\,or\,\,\,side\,\,of\,\,cube = \sqrt[3]{{Volume\,\,of\,\,cube}}$

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.