SOLUTION: A cylindrical can is being manufacturd so that its height h is 8 centimeters more than its raduis r. Determine the values for the radius to the nearest hundredth that results in th

Algebra ->  Volume -> SOLUTION: A cylindrical can is being manufacturd so that its height h is 8 centimeters more than its raduis r. Determine the values for the radius to the nearest hundredth that results in th      Log On


   

Question 324256: A cylindrical can is being manufacturd so that its height h is 8 centimeters more than its raduis r. Determine the values for the radius to the nearest hundredth that results in the can having a volume between 1000 and 1500 cubic centimeters.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a cylinder is,
V=pi%2Ar%5E2%2AH
h=r%2B8
V=pi%2Ar%5E2%28r%2B8%29
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When V=1000 cc,
V=pi%2Ar%5E2%28r%2B8%29=1000
r%5E3%2B8r%5E2=1000%2Fpi
r%5E3%2B8r%5E2-1000%2Fpi=0
I used the cubic equation solver at www.1728.com/cubic.htm to get the roots of the cubic equation (two roots are complex, the remaining root is real).
r=+4.96cm
h=r%2B8=12.96cm
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When V=1500 cc,
r%5E3%2B8r%5E2-1500%2Fpi=0
r=+5.87cm
h=+13.87cm
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(4.96+%3C=+r+%3C=+5.87)
(12.96+%3C=+h+%3C=+13.87)
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