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: To solve this particular type of question first we need to convert the speed of the river in meters per minute. Then we have to proceed by finding the volume taking the distance covered in one metre as the length. Finally we have to convert the volume into litres to find out the desired answer.

Complete step-by-step answer:

Speed of river in km per hour = 2km/hr
Speed of river in meter per minute = $2 \times \dfrac{{1000}}{{60}} = \dfrac{{100}}{3}m/\min $( multiplying with $\dfrac{{1000\operatorname{m} }}{{60\min }}$ )
(B)Breadth = 40m
(H)Height=3m
Since the water travels $\dfrac{{100}}{3}m/\min $ , therefore the length it covers in one minute = $\dfrac{{100}}{3}m$
To find the volume of water travelled in one minute we need to apply the formula of the volume of a cuboid assuming the river is cuboidal shaped ,
$volume = l \times b \times h$
$volume = \dfrac{{100}}{3} \times 40 \times 3 = 4000{m^3}$
Since $1litre = \dfrac{1}{{1000}}{m^3} \Rightarrow 1{m^3} = 1000litres$
Therefore water that falls in 1 minute $ = 4000 \times 1000 = 4000000{\text{ litres}}$

Note: Familiarize with the concept of conversion of speed of the river into the length of the cuboid in such types of questions. Note that the shape of the river is not given but we take it cuboidal for a small instance of water travelling in one minute. Remember to convert the volume in litres as the water is a liquid and any liquid should be measured in litres.