Rates of change - Swimming pool problem

[InterserveVB]

Does anyone know how to do this?

Problem:
We wish to find the change in the volume of a 20-foot-wide pool as it fills up with water. A cross-section of the pool is shown below.

Express dV/dt in terms of h, V, and dh/dt


What additional information do you need to find dh/dt at t=10 minutes?

 

[stapel]

Assuming the top-view shape to be something regular like a rectangle, then the change in volume is going to be the change in the cross-sectional area, times the height. So you should at least be able to get started (symbolically, anyway) with coming up woth functions relating the height to the cross-sectional area, and thus to the volume.

It looks like you'll have two functions, since obviously the height-and-area relationship is going to change discontinuously when the height gets to 20 - 4 = 16 feet.

For the first part, you could use the "area of a trapezoid" formula, with the height and upper "base" related (using similar triangles to find that relationship), and then switch to "that trapezoid, plus" a (much simpler) relationship between height and area for the rectangular part at the top.

I don't think there's enough information to solve this numerically, since you're not given any rates of change. And I have no idea what they're expecting you to come up with at "t = 10 minutes".

If you get stuck, please reply showing how far you've gotten. Thank you.

Eliz.

 

[InterserveVB]

volume

I know that the volume of a trapazoid is 1/2(b1 +b2)h, but how do I find the volume of the pool using this? I want to come up with a volume equation for the pool.