A rectangular swimming pool is 50 meters long and 25 meters wide. Its depth is always the same along its width but linearly increases along its length from 1 meter at one end to 4 meters at the other end. How much water (in cubic meters) is needed to completely fill the pool?
I am not able to visualize the swimming pool as described. What exactly is meant by depth remaining same along the width ? how is that measured ?
Depth along the length should be like this i guess, but now how to incorporate depth along the width ?
The shape is a trough. Imagine that the shape you drew is a cross section of the trough. Practically, this means that the volume will be $25\times A$ where $A$ is the area of the drawn figure.
To get the area we can fill in the missing triangle in the diagram, calculate the area of the resulting rectangle and then subtract the area of the triangle that we added to get the value of $A$.
Filling in the triangle gives $A+\text{ area of triangle}=4\times 50=200$
The triangle has height $3$ and base $50$ so its area is $75$.
Therefore, the area of the trapezoid in the diagram is $200-75=125$ and the volume of the trough is $25\times 125=3125$.