Question

Volume of a cylindrical tank having 7 meter diameter is 770 cubic meters, then find height of the tank.

Answer 1

Hint: First of all write the radius of the tank as half the diameter. Then, substitute the value of the volume of the tank, radius of the tank, and the value of $\pi = \dfrac{{22}}{7}$ to find the value of the radius of the tank in the formula $V = \pi {r^2}h$, where $V$ is the volume, $r$ is the radius and $h$ is the height of the tank.

Complete step by step Answer:

We are given that the volume of the tank is 770 cubic metres and the height of the tank is 7 metre.
The tank is cylindrical in shape.
We will apply the formula of the volume of the cylinder to find the height of the cylindrical tank.
It is known that the volume of the cylinder is given as \[\pi {r^2}h\], where r is the radius of the cylinder.
That is \[V = \pi {r^2}h\], where $V$ is the volume, $r$ is the radius and $h$ is the height of the tank.
We know that radius is half the diameter.
If the diameter of the tank is 7m then the radius of the tank is $\dfrac{7}{2}m$.
On substituting the value $\dfrac{7}{2}$ for radius, 770 for volume, $\dfrac{{22}}{7}$ for $\pi $, in the formula of volume of cylinder, we will get,
$770 = \dfrac{{22}}{7}{\left( {\dfrac{7}{2}} \right)^2}h$
On simplifying the expression, we get,
$
  770 = \dfrac{{22}}{7}\left( {\dfrac{7}{2}} \right)\left( {\dfrac{7}{2}} \right)h \\
   \Rightarrow 770 = 11\left( {\dfrac{7}{2}} \right)h \\
$
Cross multiply and the solve the equation,

$
  h = \dfrac{{770 \times 2}}{{11}} \\
  h = 140m \\
$
Hence, the height of the cylindrical tank is 140m.

Note: Use $\pi = \dfrac{{22}}{7}$ to avoid tricky calculations. Volume of the tank is the capacity of the tank. Volume is always measured in cubic units. The volume of cylinder is $V = \pi {r^2}h$