Question

A river 3m deep and 40m wide is flowing at the rate of 2km per hour. How much water will fall into the sea in a minute?

Answer 1

Hint: First, we will convert the given speed in metre per minute to get the length of river in metre. Then, by using the formula of volume V of the cuboid as the river is flowing in form of that to get the volume of the river as $V=l\times b\times h$. Then, we are asked the question to get the volume in litres for which we need another conversion between meter cube and litre as $1{{m}^{3}}=1000l$, we get the desired answer in litres.

Complete step-by-step answer:
In this question, we are supposed to find the amount of water that falls into the sea in a minute when the river is 3m deep and 40m wide and flowing at the rate of 2km per hour.
So, before proceeding for this, we must know the following conversions to go further to get the answer as:
1km=1000m
1 hour=60 minute
So, we get speed of the river in metre per minute as:
$2\times \dfrac{1000}{60}=\dfrac{100}{3}$
So, we get the length that the river covers in one minute as $\dfrac{100}{3}m$.
Also, in the question, we are given with the breadth as 40m and height as 3m.
Now, by using the formula of volume V of the cuboid as river is flowing in form of that to get the volume of river as:
$V=l\times b\times h$
Then, by substituting the value of length l as $\dfrac{100}{3}m$, breadth b as 40m and height h as 3m, we get the volume of river as:
 $\begin{align}
  & V=\dfrac{100}{3}\times 40\times 3 \\
 & \Rightarrow V=4000{{m}^{3}} \\
\end{align}$
So, we get the volume of water in the river as 4000 metre cube.
Now, we are asked in the question to get the volume in litres for which we need another conversion between meter cube and litre as:
$1{{m}^{3}}=1000l$
So, by using the above conversion, we get the amount of water in litres for 4000 metre cube as:
$\begin{align}
  & 4000{{m}^{3}}=4000\times 1000l \\
 & \Rightarrow 4000{{m}^{3}}=4000000l \\
\end{align}$
Hence, we get the amount of water falling into the sea per minute as $4000000l$.

So, the correct answer is “Option A”.

Note: Now, to solve these types of questions we need to know some of the basic conversions beforehand so that we can easily proceed in these types of questions. Then, some of the basic conversions are:
$\begin{align}
  & 1{{m}^{3}}=1000l \\
 & 1km/hr=\dfrac{1000}{60}m/\min \\
\end{align}$