well, the surface area question you asked me is too rudimentary(anyone with some background in calculus and geometry will grasp it) so instead ill give you volume which is alittle more interesting.

imagine a height of a cone of "h"

divide the cone in to infinite many flat cylinders. so each cylinder height would be h/n

now if we suppose the radius of the bottom surface of the cone as "r" and of course the radius at the other end of the cone as "x" then by the proportion formula

x:r =h/n:h

x=r/n

so the radius from the top to the bottom will be in a series:

r/n,2r/n,....,(n-1)r/n

so the volume of each cylinder down along the cone is:

so we add them all up which is an infinite series, which i think you can do it yourself.

which will give the result,

now finish the last part i left out for you ,genius