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Given that length $\left( l \right)$ of the rod is $1m$, i.e. $100cm$ and volume of the rod $(V)$ is $1386c{m^3}$.

And we know that the formula for a cylindrical rod is: $V = \pi {r^2}l = \dfrac{{\pi {d^2}l}}{4}$

Where ‘$r$’ is radius and ‘$d$ ‘is the diameter of the cylinder

Let’s put all the given values in the formula and see what we get

$ \Rightarrow 1386 = \dfrac{{\pi {d^2} \times 100}}{4}$

As we know that$\pi = 3.141$, putting this value in the equation we get our equation as

$ \Rightarrow 1386 = \dfrac{{3.141 \times {d^2} \times 100}}{4}$

Now let’s simplify this to get the value of the diameter

$ \Rightarrow {d^2} = \dfrac{{1386 \times 4}}{{3.141 \times 100}}$

$ \Rightarrow {d^2} = \dfrac{{1386}}{{3.141 \times 25}}$

Taking the square-root of left and right-hand sides, we can write it like:

$ \Rightarrow d = \sqrt {\dfrac{{55.44}}{{3.141}}} \approx \sqrt {17.65} $

$\Rightarrow d = 4.2012cm$

This value will be the diameter of the required Iron rod. You can easily check the answer yourself by putting this value of diameter in the formula and calculating the volume.

In Mensuration, never forget to notice the units of all the given data. Always convert the units in the same format before starting the solution. The alternative approach could be to use the formula $V = \pi {r^2}l$ and then finding the diameter after solving it for ‘$r$’.