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physicsernaw
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Homework Statement
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.
Homework Equations
SA = pi*r^2 + pi*r*l where l is the slant height of the cone.
V = 1/3pi*r^2*h = 100
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?