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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.

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Last updated date: 21st Apr 2024
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Answer
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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.

Complete step by step answer:
It is given that the diameter of the cylindrical tank is 14 m.
Therefore, the radius is equal to 7 m.
Capacity of the tank is determined by its volume.
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)
Comparing both (1) and (2) we get
$\pi {r^2}h = 2156$
Substituting the value of 7 for$r$ and $\dfrac{{22}}{7}$for$\pi $.
$\begin{array}{l}\pi {r^2}h = 2156\\ \Rightarrow \dfrac{{22}}{7} \times {7^2} \times h = 2156\\ \Rightarrow \dfrac{{22}}{7} \times {7^2} \times h = 2156\\ \Rightarrow 154h = 2156\\ \Rightarrow h = \dfrac{{2156}}{{154}}\\ \Rightarrow h = 14\;{\rm{m}}\end{array}$
Hence, the required depth (height) of the cylinder is 14 m.

Note: Here we have to determine the required depth of the cylindrical tank for the given volume. Since the radius of the cylindrical tank is known, from that we can calculate the volume of the cylinder. The capacity of the cylinder is given. Thus, by comparing the calculated volume with the given volume we can easily calculate the required depth of the cylinder.