SOLUTION: A new Japanese restaurant is pricing a koi pond. A 4 foot deep, 8 foot radius circular pond looks nice, but requires over 6000 gallons of water. The owner only wants a 5000 gallon

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Question 924471: A new Japanese restaurant is pricing a koi pond. A 4 foot deep, 8 foot radius circular pond looks nice, but requires over 6000 gallons of water. The owner only wants a 5000 gallon pond, but assumes that will be too small. You suggest reducing the radius by half a foot, but the owner scoffs that 5999.5 gallons is no better. You explain there are nearly 7.5 gallons in each cubic foot, but the owner still thinks you are only saving 3.75 gallons.
Since the volume of the pond is given by 4pir^2 , use the power rule to explain why you are saving about 200 times as much as the owner's last estimate.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
4%2Api%2Ar%5E2=5000%2F7.4805
r%5E2=5000%2F%284%2Api%2A7.4805%29
r=sqrt%285000%2F%284pi%2A7.4805%29%29

You can give the resulting calculation result for what radius equates to the 5000 gallon limit that the owner wants.

r=7.29 feet

The volume if radius is 7.5 feet:
4%2Api%2A7.5%5E2%287.48%29=5287 gallons. This is more than 5000.

Use a value closer to the 5000 gallon limit which the owner wants, and use the 7.39 foot radius. This is 7 feet 4 inches (2/3) of an inch fraction.

1 gallon is 7.4805 cubic feet. (Google used)