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.