Question

A cubical vessel is 10m long and 8m wide. How high must it be made to hold 380 cubic meters of a liquid?

Answer 1

Hint: In this question the height is to be calculated of the cubical vessel, use the direct formula for the volume of cube which is $V = lbh{\text{ }}{{\text{m}}^3}$. The volume of this cube should be taken as 380 cubic meters as it has to hold this much liquid.

Complete step-by-step answer:
The pictorial representation of the cuboidal vessel is shown above.
The length (l) of the vessel is given as 10 m and the breadth of the vessel is given as 8 m.
Now we have to calculate the height of the vessel so that it can hold 380 cubic meters of liquid.
Therefore the volume (V) of the cuboidal vessel is = 380 m3.
Now as we know the volume of a cuboidal vessel is the multiplication of length, breadth and height.
$ \Rightarrow V = lbh{\text{ }}{{\text{m}}^3}$
Now substitute the values in the above equation we have,
$ \Rightarrow 380 = 10 \times 8 \times h$
$ \Rightarrow h = \dfrac{{380}}{{80}} = \dfrac{{38}}{8} = \dfrac{{19}}{4} = 4.75$ meter.
So the height of the cuboidal vessel is 4.75 meter.
So this is the required answer.

Note: Whenever we face such types of problems it is always advisable to remember the direct formula for some basic shapes like cube, cuboid etc., as it helps to save a lot of time. The volume of the liquid that is filled eventually leads to increase in height thus this much of volume given in question is what the height needs to be calculated for.