Differeniation: related rates

  • Thread starter Alethia
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  • #1
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So I'm doing my homework and I get stuck (again) on this problem:
A swimming pool is 12 meters long, 6 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end. Water is being pumped into the pool at 1/4 cubic feet per minute, and there is 1 meter of water at the deep end.

a) What percent of the pool is filled?
b) At what rate is the water level rising?
Okay what I first did was gather all my given information. That includes all the given dimensions of the pool and dv/dt to be the 1/4 cubic feet per minute. I just need guidance through this problem or where to start... so if anybody is willing to explain to me where to begin... For instance, on part a, do I need another equation for this or is that part of b? ACtually, I don't know what I'm talking about... HELP! :tongue2:
 

Answers and Replies

  • #2
Galileo
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For part a, simply calculate the volume of the pool and calculate the volume of water in the pool. Then get the percentage. (Drawing a picture may help)

For part b, I would write down the function which gives the height of the water level as a function of the volume of water in the pool. Then differentiate that function.
 
  • #3
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Alethia said:
So I'm doing my homework and I get stuck (again) on this problem:Okay what I first did was gather all my given information. That includes all the given dimensions of the pool and dv/dt to be the 1/4 cubic feet per minute. I just need guidance through this problem or where to start... so if anybody is willing to explain to me where to begin... For instance, on part a, do I need another equation for this or is that part of b? ACtually, I don't know what I'm talking about... HELP! :tongue2:

once you've derived a formula for the volume of the empty space of the pool, i would try to get it into one variable, height. you may need to look at two seperate volumes though, the rectangle produced and the triangular shape resulting from the gradiant. from that point you can differentiate with respect to time, since you know the rate the volume is increasing you should be able to figure out the rate that height is increasing. i would suggest drawing out a diagram and digging to remember some geometry.

the first question doesn't make sense to me -- at what point in time is it refering to? if it means initially, i would try looking at the bottom of the pool and calculate the area that's already full. it says that theres 1 meter of water in the deep end.

edit: volume, not area
 

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