Question

A river 2 m deep and 40 m wide is flowing at the rate of 4.5 km per hour. How many cubic meters of water runs into the sea per minute ?

Answer 1

Hint: Consider a river as a long cuboid, which length is equal to the length of the river. We have to find the volume of a part of this cuboid.
Formula to find the volume of a cuboid with length l, breadth b and height h is written below
Volume of a cuboid \[ = {\text{ }}l*b*h\]
The length of the cuboid( whose volume we have to calculate ) has to be calculated from the given speed of flowing water. The other two dimensions of the cuboid are indirectly given in question above.

Complete step-by-step answer:
As it is given in the question that speed of the river is = 4.5 km per hour
$\therefore $ Water flowing in river in 1 hour = 4.5 km
  = 4.5 * 1000 m
   = 4500 m
Water flowing in river in 60 minutes = 4500 m
Water flowing in river in 1 minute = $\dfrac{{4500}}{{60}}$m
\[ = {\text{ }}75{\text{ }}m\]
Now the river is in the shape of a cuboid as shown

Length of cuboid = \[l{\text{ }} = {\text{ }}40{\text{ }}m\]
Breadth of cuboid = \[b{\text{ }} = {\text{ }}75{\text{ }}m\]
Height of cuboid = \[h{\text{ }} = {\text{ }}2{\text{ }}m\]
$\therefore $ Volume of water running into the river per minute = Volume of cuboid
 \[ = {\text{ }}l*b*h\]
 \[ = {\text{ 40}}*75*2\]m3
 \[ = {\text{ }}{\mathbf{6000}}{\text{ }}{{\mathbf{m}}^{\mathbf{3}}}\]

Note: Students should keep in mind to first convert all the dimensions in the same unit and then calculate the volume. And also keep in mind that we have to calculate the length of the cuboid of water for 1 min and not 1 hour.