Question

Find the height of the cylinder whose volume if $1.54m^3$ and diameter of the base is $140cm$.

Answer 1

Find the height of the cylinder

We have, volume of cylinder $=1.54m^3$

$$\begin{gathered} =1.54\times 100\times 100\times 100c{m}^3[\because 1m=100cm] \\ =1540000{cm}^3 \end{gathered}$$

Diameter of base $=140cm$

Therefore, radius of base $=\frac{140}{2}cm$

$=70cm$

Suppose, height of the cylinder is $h$

We know that the volume of the cylinder is ${\mathrm{\pi r}}^2\mathrm{h}$

So, according to the question,

$\begin{array}{rcc}\mathrm{\pi }\times {\left(70\right)}^2\times \mathrm{h}& =& 1540000\end{array}$

$$\begin{gathered} \Rightarrow h=\frac{1540000\times 7}{22\times 70\times 70}\left[\because \mathrm{\pi }=\frac{22}{7}\right] \\ \Rightarrow h=100cm \end{gathered}$$

Hence, height of the cylinder is $100cm.$