MHB How Long to Empty Lake Erie with a Cone Cup?

AI Thread Summary
Lake Erie contains 116 cubic miles of water, which converts to approximately 4.6568 x 10^11 cubic inches. A cone cup with a diameter of 2.75 inches and a height of 4 inches has a volume of about 7.9194 cubic inches. To determine how long it would take to empty the lake using this cone cup, the total volume of the lake should be divided by the volume of the cone, and then multiplied by the time taken to dump one cup, which is 2 seconds. The discussion also raises a hypothetical scenario of how the time would change if three cups were dumped every two seconds instead of one. The arithmetic needs verification, but the overall approach to solving the problem is outlined clearly.
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Lake Erie holds 116 cubic miles of water. Suppose you start dumping out the entire volume of Lake Erie using a cone cup. A typical cone cup has a diameter of 2.75 inches and a height of 4 inches. About how long would it take you to empty the lake if you could dump out one cup per 2 seconds? Use stoichiometry.
Work:

1 foot = 12 inches
1 mile = 5280 feet
1 cubic foot = 1728 cubic inches
1 cubic mile = 1.4720 x 10^11 cubic feet
1 cubic mile = 2.536 x 10^14 cubic inches

radius= 2.75/2= 1.375 inches
Volume of cone= h/3*(pi)r^2
= 4/3*(pi)(1.375)^2
= 7.9194 in^3

5280 ft/1 mile * 12 in/1 ft = 63,360 in/miles

Volume of Lake= 116 cubic miles * 63,360^3
=4.6568 * 10^11 cubic inches/miles

Note: I'm unsure how to find the time in this problem. Also, I'm not sure if my work above is correct. Thank you.
 
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I have not checked your arithmetic but assuming it is correct dividing the volume of the lake by the volume of the paper cone gives the number of times you would have to fill the cone from the lake (I will try not to become distracted by wondering where you are going to dump the water!). You are told that you dump out one cone of water every 2 seconds so multiplying the number of times you need to dump out a cone by 2 gives the number of seconds it takes.
 
HallsofIvy said:
I have not checked your arithmetic but assuming it is correct dividing the volume of the lake by the volume of the paper cone gives the number of times you would have to fill the cone from the lake (I will try not to become distracted by wondering where you are going to dump the water!). You are told that you dump out one cone of water every 2 seconds so multiplying the number of times you need to dump out a cone by 2 gives the number of seconds it takes.

This is a bit of a stretch but do you know how the problem would differ if you had to dump out three cups per two seconds rather than one cup per one second.
 
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