calc

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the volume of a cylindrical tin can with a top and a bottom is to be 16*pi cubic inces. if a minimum amont of tin is to be used to construct the can, what must be the height, in inches, of the can?

volume of cyliner is pi*r^2*h

you want to minimize surface area.

Area= 2*2PIr + h*2PIr
but h= V/Pir^2
TAke dA/dr, set to zero, solve for r.

Then solve for h in the volume equation.

I need to know how to get the total surface area of a cylinder. The way that I get the lateral area is by taking by info for example 5cm x 12cm 60x3.14x2 =376.8cmsquared but I am trying to get the total area.

• calc -

set volume=16pi, solve for r
then substitute r in for the surface area equation (2pirh+2pir^2)
take the derivative
find critical point (where derivative=0)
then make sure that is a minimum

• calc -

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• calc -

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