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

[kato1]

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.

 

[HallsofIvy]

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.

 

[kato1]

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.