5. What are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of .8L?

Answer 1

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.