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

[slayerdeus]

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?

 

[cookiemonster]

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

 

[slayerdeus]

umm okay, so 43000m*height=1/2(pi)r^2h?

 

[cookiemonster]

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

 

[slayerdeus]

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

 

[cookiemonster]

Looks right to me.

cookiemonster

 

[Physics is Phun]

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

 

[AKG]

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?