Question

Given a bottle with a Height vs. Volume graph that is created as the bottle is consistently filled with a liquid, describe the correlation between the width of the bottle and the steepness of the graph.

Answer 1

I understand this problem as follows.

We have a bottle (the bottle is empty at the beginning)

Now, as we start to fill the bottle, we do a graph of height vs volume.

Where height is the height of the liquid inside the bottle, and volume is the volume of liquid inside the bottle.

suppose that here you need a volume V to reach a height H.

Now, if we increase the width of the bottle, we are increasing the volume of the bottle.

This means that we should pour a larger volume of liquid to reach the same height as before.

V' = V + d, to reach the same height H.

Then the steepness of the graph decreases.