Question

A cuboidal water tank can hold 60,000 liters of water. If the length and breadth of the tank are 10m and 4m, find its height.
(a) 1.5m
(b) 1.6m
(c) 0.5m
(d) 1.7m

Answer 1

Hint: The volume of a tank is the amount of water it can hold. Convert the quantity in liters to meters using 1000 liters = 1\[{{m}^{3}}\]. From the volume of the cuboid formula, substitute all the values and find the height.

Complete step-by-step answer:
It is given that a cuboidal water tank can hold 60,000 liters of water. Thus it means that the volume of the cuboidal water tank is 60,000 liters.
We have been given the length and breadth of the cuboidal tank as 10m and 4m. Let us take the height of the cuboidal water tank as h.
Let length = l = 10m, breadth = b = 4m.

Now, we have been given the dimensions in meters and the volume in liters. Let us convert the quantity in liters to meters using the basics of,
1000 liters = 1\[{{m}^{3}}\]
6000 liters = 60 \[\times \] 1000 liters = 60 \[\times \]1\[{{m}^{3}}\] = 60\[{{m}^{3}}\]
Hence we can say that the volume of the cuboidal water tank = 60\[{{m}^{3}}\].
We know the formula for calculating the volume of cuboid as,
Volume of cuboid = length \[\times \] breadth \[\times \] height.
\[\therefore \] Volume of the cuboidal water tank = lbh
60 \[{{m}^{3}}\] = 10 \[\times \] 4 \[\times \] h
\[\begin{align}
  & \Rightarrow 60=40h \\
 & \therefore h=\dfrac{60}{40}=1.5m \\
\end{align}\]
Thus we got the height of the cuboidal water tank as 1.5m.
\[\therefore \] Option (a) is the correct answer.

Note: The questions are one of the most simple concepts of volume in cuboid. If you know the formula to find the volume of cuboid, then you will get the answer easily. Care should be taken to ensure that all the quantities have the same unit or make them into the same unit, as we have done for liters to meters.