Question

 An overhead water tanker is in the shape of a cylinder has capacity of 616 liters. The diameter of the tank is 5.6m. Find the height of the tank.
A. 5.5.
B. 2.5.
C. 1.55.
D. 4.5.

Answer 1

Hint: Because we are given that the overhead water tanker is in the shape of a cylinder, therefore we use the formula of volume of cylinder to calculate the capacity of the water tank which is given as \[V=\pi {{r}^{2}}h\], where r is the radius of the cylinder and the h is the height of the cylinder.

Complete step by step answer:
Given we have an overhead water tanker in the shape of a cylinder with volume 616 liters, and the diameter of the tank is 5.6m.
Therefore, given diameter d = 5.6m and Volume V= 616L
We know that, diameter is double of radius, then,
\[d=\dfrac{r}{2}\], where r is the radius of the cylinder base and d is the diameter of the base.
Substituting the value of d we get,
\[\begin{align}
  & \Rightarrow 5.6=\dfrac{r}{2} \\
 & \Rightarrow r=2(5.6) \\
 & \Rightarrow r=2(5.6) \\
 & \Rightarrow r=11.2m \\
\end{align}\]
So, we obtained the radius of the base as r = 11.2m.
Now as the volume is given, we can use the formula of volume to find out the height of the tanker.
We have Volume of the tanker as,
\[V=\pi {{r}^{2}}h\]
Substituting the values of radius r and the Volume V we have,
\[\begin{align}
  & 616=\dfrac{22}{7}{{(11.2)}^{^{2}}}(h) \\
 & \Rightarrow h=616(\dfrac{7}{22}){{(\dfrac{1}{11.2})}^{2}} \\
 & \Rightarrow h=616(\dfrac{7}{22})(0.0079) \\
 & \Rightarrow h=616(0.3181)(0.0079) \\
 & \Rightarrow h=1.55m \\
\end{align}\]
Hence, the height of the tanker is 1.55m, which is option(c).

Note: The possibility of error in this question is using different units in different given values which would be wrong because if you use volume in liters per meter and diameter or the height in centimeter then it would definitely lead to a wrong answer. So always try to use a single unit of calculation.