Answer

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}} $

**:**

__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.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

10 examples of evaporation in daily life with explanations

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

Difference Between Plant Cell and Animal Cell