Question

Diameter of a cylindrical tank is 7 m. If the volume of the tank is 770 m3, then find the height of the tank?
A.50m
B.20m
C.50cm
D.200m

Answer 1

Hint: Diameter and volume of the cylinder is given.
Find the radius of the cylinder from diameter I.e. $ r = \dfrac{D}{2} $
Substitute these values in the formula for volume of a cylinder:
 $ V = \pi {r^2}h $
And find the value of h i.e. height of the tank in the given question.

Complete step-by-step answer:
Diameter of cylinder (D) = 7 m
 $ \Rightarrow $ radius of cylinder (r) = $ \dfrac{D}{2} = \dfrac{7}{2}m $
Also, volume of tank (V) = 770 m3

As we know, volume of a cylinder with radius (r) and height (h) is given by:
 $ V = \pi {r^2}h $
 $ \Rightarrow h = \dfrac{V}{{\pi {r^2}}} $
Putting r = $ \dfrac{7}{2}m $ and $ V = 770{m^3} $ to find the height of tank:
 $ \begin{gathered}
   \Rightarrow h = \dfrac{{770}}{{\dfrac{{22}}{{l{7}}} \times \dfrac{{{7}}}{2} \times \dfrac{7}{2}}} \\
  h = \dfrac{{770 \times 2}}{{11 \times 7}} \\
  h = 20m \\
\end{gathered} $
So, the height of the given tank is 20m and option B is correct.

Note: Volume of a cone is one third of the volume of a cylinder with same dimensions:
 $ \begin{gathered}
  {\text{Volume of cone = }}\dfrac{1}{3} \times {\text{ area of cylinder}} \\
   \Rightarrow {{\text{V}}_{cone}} = \dfrac{1}{3} \times \pi {r^2}h \\
\end{gathered} $