Total area of open cyclinder is:

A(r) =    where r is radius and L is length of side



The volume is:

V(r) = 



We can relate L to r by the given information:

   ===>  



So 





which reduces to:





Now the derivative of V with respect to r is:





Setting dV/dr to 0 and solving for r,   cm 



Check by plugging in some values near 7.0cm for r, and compute corresponding volume:

r = 6.8  ==>  L = 7.4  ==>  V = 1074.9cm^3

r = 7.0  ==>  L = 7.0  ==>  V = 1077.6cm^3   <<< max capacity

r = 7.2  ==>  L = 6.6  ==>  V = 1076.5cm^3



 

Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 Recommend Graphing V =  231r - (pi/2)r^3 as a check for r = 7cm  when Volume is at its Maximum

Obvious max is reached at 7cm (to nearest whole number)

www.padowan.dk/download has an excellent graphing capabilities.



Graphing y = 231x - (pi/2)x^3    (y the volume, x the radius of the Cylinder)



 

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