Posted by Adam on Sunday, December 12, 2010 at 8:59pm.
5. What are the dimensions of the lightest opentop right circular cylindrical can that will hold a volume of .8L?

AP CALCULUS PLEASE HELP DUE TOMORROW!  drwls, Sunday, December 12, 2010 at 10:04pm
That depends upon how thick you make the walls of the cone. They should have asked for the minimum surface area cone with that volume.
The surface area of a cone is:
A = pi s r
= pi*sqrt(r^2 + h^2)*r
where s is the slant height and h is the height of the axis.
The cone volume must satisfy (1/3)pi*r^2*h = 800 cm^3, so
h = 2400/(pi*r^2)
Write A as a function of r only and differentiate A(r). Set the derivative equal to zero and solve for r.
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