Question

A river $ 2m $ deep and $ 45m $ wide is flowing at the rate of $ 3km $ per hour. Find the volume of water that runs into the sea per minute.

Answer 1

Hint: Here we will find the volume of the water flows first by finding the area in terms of the product of the depth and width of the river and then multiplying it with the rate of flow of the water. Convert all the given values in the same system of units before placing them in the formula and then simplify for the resultant required value.

Complete step-by-step answer:
Given that: the rate of flow of water is $ 3\dfrac{{km}}{{hr}} $
Also, given that the depth of the river is $ = 2m $
Width of the river is $ = 45m $
Now, the area of the cross-section of the river is given by $ = 45 \times 2 $
Find the product of the terms of the above expression –
the area of the cross-section of the river is given by $ = 90{m^2} $ …… (A)
Rate of flow of the water is $ 3\dfrac{{km}}{h} $
Convert the above expression given in kilometer per hour in meters per second
Rate of flow of the water is $ = \dfrac{{3 \times 1000}}{{60}}\dfrac{m}{{\min }} $
Remove common factors from the numerator and the denominator.
Rate of flow of the water is $ = 50\dfrac{m}{{\min }} $ …… (B)
The flow of water per minute $ = 90 \times 50 $
Simplify the above expression finding the product of the terms –
The flow of water per minute $ = 4500 $ $ {m^3} $ .
So, the correct answer is “ $ 4500 $ $ {m^3} $ ”.

Note: Always be careful about the system of units and know the basic conversational relations between the different terms. Also, do not forget to place the appropriate unit after the values received at the end of the solution. Remember one min and one hour differs a lot. $ 1{\text{ hour = 60}}\;{\text{min}} $ .