SOLUTION: Lucy has a hemispher-shaped goldfish pond in her backyard. The pond has circumference of approximately 11.9 feet. Part A- The pond has a population density of approximately 3.6 c

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Question 1080417: Lucy has a hemispher-shaped goldfish pond in her backyard. The pond has circumference of approximately 11.9 feet.
Part A- The pond has a population density of approximately 3.6 cubic feet of water for each goldfish. How many goldfish are in Lucy's pond? Show all your work and/or explain your reasoning.
Part B- Lucy found a website that recommends 5.3 cubic feet of water for the first goldfish and 1.6 cubic feet of water for each additional goldfish. Lucy increases the number of goldfish in her pond to the maximum number based on the recommendations for the website. What is the new population density of the pond? Show all your work and/or explain your answer.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r, radius of upper pond surface

2pi%2Ar=11.9
r=5.95%2Fpi

pond volume: %281%2F2%29%284%2F3%29pi%2Ar%5E3
%282%2F3%29pi%2Ar%5E3
%282%2F3%29pi%2A%285.95%2Fpi%29%5E3

14.2285 cubic feet


Part A -
3.6 cubic feet per goldfish
14.2285%2F3.6=3.952
Maybe 4 goldfish


Part B -
14.2285-5.3=8.9285 cubic feet after 1 goldfish
-
8.9285%2F1.6=5.58%2Agoldfish---best to round down. Rounding up to 6 fish could exceed what the website recommends.

Use 5 goldfish after the first one, for a total of 6 goldfish