Question

A water tank is filled with 104,000 liters of water. Its length and breadth are 800 cm and 650 cm respectively. What is the height of the water tank in cm?

Answer 1

Hint: We will convert the volume of the tank from liters into cubic cm. Then we will look at the formula for the volume of a water tank. The water tank is a cuboid, so we will use the formula for the volume of a cuboid. We are given the values of length and breadth. We will substitute the given values in the formula and solve for the unknown variable, that is height.

Complete step by step answer:
The volume of the water tank is given as 104,000 liters. The length of the tank is 800 cm and the breadth of the tank is 650 cm. Since, the length and breadth are given in cm, we will convert the volume of the tank from liters to cubic cm. Now, we know that $1\text{ liter = 1000 c}{{\text{m}}^{3}}$. So, the volume of the tank in cubic cm will be,
$\begin{align}
  & \text{Volume (V) = 104000 liters} \\
 & \text{=104000}\times \text{1000 c}{{\text{m}}^{3}}
\end{align}$
The water tank is a cuboid. Hence, we will be using the formula for the volume of a cuboid, which is as follows,
$\text{Volume of a cuboid = length }\times \text{ breadth }\times \text{ height}$
We have the following values: $\text{V = 104000}\times \text{1000 c}{{\text{m}}^{3}}$, $l=800\text{ cm}$ and $b=650\text{ cm}$. Substituting these values in the above formula, we get
$104000\times 1000=800\times 650\times h$
Rearranging the above equation and solving for $h$, we get
$\begin{align}
  & h=\dfrac{104000\times 1000}{800\times 650} \\
 & =\dfrac{104000}{8\times 65} \\
 & =\dfrac{13000}{65} \\
 & =\dfrac{1000}{5} \\
 & =200\text{ cm}
\end{align}$
Therefore, the height of the water tank is 200 cm.

Note:
The conversion of the volume from liters to cubic cm is essential, since the length, breadth and height are in cm. Realizing the shape of the given object, in this case- a water tank, is necessary so that we can use the correct formula for the volume of the given object. The calculation for such types of questions needs to be done carefully, since it involves large numbers, there is a chance that we might miss out a zero here and there.