Question

A river $1.5m$ deep and $36m$ wide is flowing at the rate of $3.5km/hr$ . Find the amount of water (in cubic meters) that runs into the sea per minute.

Answer 1

Hint: Here we are asked to find the amount of water that runs per minute using the given data. As we can see that all the given values are in different units, we will first try to convert them for our convenience. Then we will first find the speed of the flow of the water. Then the required amount of water that runs into sea per minute can be found by the product of the water flow’s speed and the area of the river.

Formula used:
Formula that we need to know:
$1000m = 1km$
$1hr = 60\min $

Complete answer:
Since we know as given in the question:
Depth of the river is $1.5m$ and the width of the river $36m$
Using the conversion of units, since $1$ hour is equal to $60$ minutes and $1km$ contains $1000m$
Since the flow rate of river as given in the question $3.5km/hr$
Now calculating the given values into the desired values is like converting $3.5km/hr$ into $m/\min $ as the volume required is in ${m^3}$ .
Now we multiply the given quantities into the desired by the following calculation $\dfrac{{\left( {3.5 \times 1000} \right)}}{{\left( {1 \times 60} \right)}}m/\min $
On solving further, we get
$ = \dfrac{{350}}{6}m/\min $
Now this is the speed of flow of water.
Now the amount of water that runs into the sea per minute
Flow of river $ \times $ area of the river
area of river $=1.5m \times 3.6m$
$= 5.4{m^2}$
The amount of water running $ = $ speed $ \times $ area of water.
$ = \dfrac{{350}}{6} \times 1.5 \times 36$
$ = 350 \times 1.5 \times 6$
\[ = 3150{m^3}/\min \]
Now the water that runs into the sea per minute is equal to \[3150{m^3}/\min \] . Which is the desired answer for the given question.
As the speed is given in the km/hr but the answer is expected in ${m^3}$ so we have to do the necessary conversion

Note:
In this problem, we have been asked to find the amount of water, we know that the unit of amount of water is nothing but volume which will be in cubic meters so it is necessary to convert the given values to the desired units. Also, the calculation must be made correct in order to avoid mistakes.