Question

A river 2m deep and 43m wide is forwarding at the rate of $5km/hr$. Find the quantity of water that runs into the sea per minute.

Answer 1

Hint: Find length of water flow per minute. This gives the length of the cuboid. Then find the volume of the cuboid using the formula $V=lbh$ . Where l, b and h are the length, breadth and height of cuboid respectively.
Convert the flow rate of water in km/min








Complete step-by-step answer:
As from questions we have
Width of river $=43m$
Depth of river $=2m$
We have to find the amount of water that runs into the sea per minute.
As flowing rate of river $=km/hr$
So, we have to convert it $km/\min $
So flowing rate $\begin{align}
  & \\
 & =3\times \dfrac{1km}{60\min } \\
 & =\dfrac{1}{20}km/\min \\
\end{align}$
So, the length of water travelled in one minute.
We use $l=vt$
Where l is length, $v$ is rate of flowing and $t$ is time.
So
$l=\dfrac{1km}{20\min }\times 1\min $
Here min in numerator cancel out with the denominator.
As water run into sea for $1\min $
$\begin{align}
  & \therefore \text{ l=}\dfrac{1}{20}\times 1000m \\
 & As\text{ 1km = 1000m} \\
\end{align}$
So, Length of water enter in sea in one minute
$l=50m$
So, volume of water = volume of cuboid
     Volume of water = (length of water flow in one minute) (breadth)(height)
$\begin{align}
  & l\times b\times h \\
 & l=50m \\
 & b=43m \\
 & h=2m \\
 & \therefore volume=50\times 43\times 2{{m}^{3}} \\
 & \text{ }volume=4300{{m}^{3}} \\
 & \\
\end{align}$

Note: We can convert $\dfrac{km}{h}$ to $\dfrac{m}{s}$ by simply multiplying with$\dfrac{5}{18}$.
$\dfrac{1km}{h}=\dfrac{5}{18}\times \dfrac{m}{s}$
Change the unit as per the question and take care of the unit of volume i.e. ${{m}^{3}}$ .
Also, we can answer in unit litre by using the relation $1000\text{ litre = 1}{{\text{m}}^{3}}=1000d{{m}^{3}}$
Hence volume of water that enter in sea in one minute $4300000\text{ d}{{\text{m}}^{3}}=4300000\text{ litre}\text{.}$