How Deep Does a Lake's Water Level Drop Annually Due to Local Consumption?

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Homework Help Overview

The discussion revolves around calculating the annual drop in water level of a lake due to local consumption, specifically focusing on the water usage of a town's population. The problem involves understanding volume, area, and height relationships in a geometric context.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore different methods to relate the volume of water consumed to the lake's surface area and height. Questions arise regarding the appropriate formulas and the interpretation of the lake's dimensions.

Discussion Status

There are multiple interpretations of the calculations involved, with participants providing different approaches to derive the height of water level drop. Some guidance has been offered regarding the relationship between volume and area, but no consensus has been reached on the correct calculations.

Contextual Notes

Participants are working under the assumption that evaporation and other factors are negligible, focusing solely on population water usage. There is also a discussion about the correct conversion of units and the implications of annual calculations.

slayerdeus
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An average family of four uses roughly 1200 liters (about 300 gallons) of water per day. (one liter = 1000 cm3.) How much depth would a lake lose per year if it uniformly covered an area of 43 square kilometers and supplied a local town with a population of 43000 people? Consider only population uses, and neglect evaporation, etc.

Where do I even start? I thought of viewing it as a cylinder but, there is no height. uh?
 
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You're solving for the height. You don't know the shape of the lake, only the size of its footprint. But the footprint's size times the height will yield the volume. So use the population of the town to figure out the volume, then solve for height.

cookiemonster
 
umm okay, so 43000m*height=1/2(pi)r^2h?
 
No.

Volume = Area*height.

What's the volume of water that 43000 people use? What's the area of the lake? Solve for height.

cookiemonster
 
The volume of water would be (43000 people/4)*(1200 L)*(1000 cm^3/L)= 1.29e10 cm^3
Area = (43km^2)(100000 cm/km) = 4300000 cm^2
*btw the final answer must be in cm

h = 1.29e10 cm^3/4300000 cm^2
h = 3000 cm
 
Looks right to me.

cookiemonster
 
30 metre?? sheesh. that's A lot of water. when I did I I got .03cm for the height.
I will double check my work. If I am not mistaken your area is not correct. if the area is 43km^2 then the area in cm is (root(43)*100000)^2 which equals 4.3E11
Someone please correct me if I'm wrong
 
This is definitely wrong, slayerdeus and cookiemonster. You haven't taken into account that there are 365 days in a year.

height/year
= height/volume * volume/year
= height/volume * volume/day * day/year
= height/volume * (volume/day)/person * number_of_people * day/year
= height/volume * (volume/day)/family * family/person * number_of_people * day/year
= 1/area * 1200 L * 1000cc/L * 1/4 * 43000 * 365
= 1/43 km^2 * (1km^2/10,000,000,000 cm^2) * 1,200,000/4 * 43000 * 365
= 10.95 cm/yr

A much more reasonable answer, don't you think?
 

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