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: Convert the speed of the river from km per hour to metre per minute. Then calculate the volume of water that flows in a minute, by assuming the river flows in the shape of a cuboid.

Complete step by step answer:
It is given, Speed of the river = 2 km per hour.

Now, we know,

$\begin{align}

  & 1\text{ km per hour = }\frac{1\text{ km}}{1\text{ hour}} \\

 & \text{ = }\frac{1000\text{ m}}{60\operatorname{minutes}} \\

 & \text{ = }\frac{50}{3}\text{ m per min}\text{.} \\

\end{align}$

Thus, we can say that, the speed of the river

$\begin{align}

  & =\text{2 km per hour} \\

 & \text{= 2 x }\frac{50}{3}\text{ m per minute} \\

 & \text{= }\frac{100}{3}\text{ m per minute} \\

\end{align}$

It is given that,

Depth of the river = 3 m.

Width of the river = 40 m.

Now, if we assume the water in the river flows in the shape of a cuboid, we can say that,
In a minute, the length of the river $=\text{ }\frac{100}{3}\text{ m}\text{.}$

 We know the formula of a volume of a cuboid = l x b x d, where ‘l’ is the length, ‘b’ is the breadth and ‘d’ is the depth of the cuboid.

Putting the values l $=\text{ }\frac{100}{3}\text{ m}\text{.}$, b = 40 m. and d = 3 m in the above formula, we get,

Volume of the water flowing through the river in 1 minute

$\begin{align}

  & =\text{ }\left( \frac{100}{3}\text{ x 40 x 3} \right)\text{ }{{\text{m}}^{3}} \\

 & =\text{ 4000 }{{\text{m}}^{3}} \\

\end{align}$

Hence, $4000\text{ }{{\text{m}}^{3}}$of water will flow into the sea from the river in 1 minute.


Note: The given problem can only be solved if the underlying assumption is that the river flows in the shape of a cuboid. Although, practically this assumption is not very much valid, but it is being assumed here for the sake of computational simplicity.