SOLUTION: A square fountain has an area of 16 square feet. A flower garden is planted around the fountain. If the garden extends 8 feet beyond the fountain, what is the area of the garden.

Question 28542: A square fountain has an area of 16 square feet. A flower garden is planted around the fountain. If the garden extends 8 feet beyond the fountain, what is the area of the garden.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You have a circle inside a circle.
The inner circle has area =(pi)r^2=16
r^2=16/(pi)
r=4/sqrt(pi)
The outer circle has radius "8+[4/sqrt(pi)]
The whole outer circle has area (pi)[8+4/sqrt pi]^2
=pi[64+(64/sqrt pi) + (16/pi)]=64pi +64 sqrt pi + 16
Subtract the inner area from the whole area to get the
area of the garden, as follows:
64pi+64sqrt(pi)+16 - 16 = 64pi+64sqrt(pi) is the area of the garden.
Cheers,
Stan H.
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