SOLUTION: Maths question help 5. Derive a formula for finding the Surface Area as a function of the radius, with the can still modelled as a cylinder. State your formula in simplest form.

Question 482080: Maths question help
5. Derive a formula for finding the Surface Area as a function of the radius, with the can still modelled as a cylinder. State your formula in simplest form.
6. Differentiate the function and be sure to simplify your answer. Now use the derivative function to find the value of the radius when the Surface Area is a minimum, and then find the minimum Surface Area.
Part C – Real Can
The soft drink can, however, is not actually a perfect cylinder.

8. Repeat steps 5 and 6 in Part B, modelling the can with a double layer of metal on the top, but with a hemispherical indent in the base.

Answer by richard1234(5390) (Show Source):
You can put this solution on YOUR website!
5. Assuming that the object is a cylinder and the height is constant (b/c it's a function of the radius) we have

Since A is a function in terms of r,

Finding the minimum surface area is trivial, set r = 0. Hopefully this is what your problem meant...

You'll have to describe #8 a little more clearly, since my first thought is to double the area of the top, and maybe cut out a hemisphere on the bottom, but I am not 100% sure. Either way, just find the surface area (A) in terms of r, find dA/dr then set it to zero to find possible extrema.