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

Question 1033154: 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 rothauserc(4718) (Show Source): You can put this solution on YOUR website!
First, calculate the volume of the hemisphere which is 1/2 the volume of a sphere
:
V = (1/2) * ((4/3) * pi * r^3) = (2/3) * pi * r^3
:
note that pi = (22/7). C = 2*pi*r, r = 11.9 / (2*pi*) = 1.893181818 approximately 1.89 feet, where C is circumference and r is radius
:
V = (2/3) * (22/7) * (1.89)^3 = 14.145516 approx 14.15 cubic feet
:
*******************************************************************
Part A
number of goldfish = 14.15 / 3.6 = 3.930555556 approx 4 goldfish
*****close enough to support 4 goldfish******
*******************************************************************
Part B
number of goldfish = ((14.15 - 5.3) / 1.6) + 1 = 6.53125 approx 6 goldfish
****not enough to support 7 goldfish******
********************************************************************
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