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# A cylindrical tank has a capacity of 2156 m3 and diameter of the base is 14 m. If $\pi = \dfrac{{22}}{7}$, find the depth of the tank.

Last updated date: 21st Apr 2024
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Hint: In this problem, the volume of the cylindrical tank is given so we have to compare that volume with the volume formula of cylinder which can be expressed as $\pi {r^2}h$, here r is the radius of the cylinder and h is the height of the cylinder. Since the diameter of the cylinder is given, we can find the radius. After that by substituting the value of r and the $\pi$ we get the required height of the cylinder.

Volume of the cylindrical tank $= 2156\;{{\rm{m}}^3}$ (1)
It is known that the formula of the volume of a cylinder $= \pi {r^2}h$ (2)
$\pi {r^2}h = 2156$
Substituting the value of 7 for$r$ and $\dfrac{{22}}{7}$for$\pi$.
$\begin{array}{l}\pi {r^2}h = 2156\\ \Rightarrow \dfrac{{22}}{7} \times {7^2} \times h = 2156\\ \Rightarrow \dfrac{{22}}{7} \times {7^2} \times h = 2156\\ \Rightarrow 154h = 2156\\ \Rightarrow h = \dfrac{{2156}}{{154}}\\ \Rightarrow h = 14\;{\rm{m}}\end{array}$