1. The problem statement, all variables and given/known data We want to make a conical drinking cup out of paper. It should hold exactly 100 cubic inches of water. Find the dimensions of a cup of this type that minimizes the surface area. 2. Relevant equations SA = pi*r^2 + pi*r*l where l is the slant height of the cone. V = 1/3pi*r^2*h = 100 3. The attempt at a solution I solve l in terms of h and r. l = sqrt(r^2 + h^2) Then I solve h in terms of r in the volume, and I get: h = 300/pi*r^2 plugging this equation for h back in the equation for l, I get: l = sqrt(r^2 + 300/(pi*r^2)) SA(r) = pi*r^2 + pi*r*sqrt(r^2 + 300/(pi*r^2)) Then taking the derivative and setting it equal to zero: SA'(r) = 2pi*r + pi*sqrt(r^2 + 300/(pi*r^2)) + 1/2*pi*r/(sqrt(r^2 + 300/(pi*r^2)))*(2r + 600/(pi*r^3)) = 0 Instead of trying to solve that ugly thing myself I plugged it into wolfram and it said no real solutions exist so I'm obviously doing something wrong. Any help pleasE?