Two applications, PPPL NUF (top choice) and SULI (PPPL and Los Alamos). Really want to do plasma, and my research group has some collaborators at PPPL, so I could start a project there and continue it during the school year (if necessary). Crossing my fingers! (Haven't heard anything yet >.>)
I disagree. This would be analogous to a volume of revolution--rather, we are taking a surface area. Each disk has radius r and therefore circumference 2*pi*r; since r varies as a function of h, we can evaluate the integral of 2*pi*r*dh from 0 to 4.
Surface area of a cone--inconsistency?
Geometry tells us that the surface area of a cone with a circular base is
SA = \pi rs
where s is the slant height of the cone, or
SA = \pi r \sqrt{r^2 + h^2}
Take a cone with a circular base of radius 1 and a height of 4. This formula tells us...