Optimization - Find dimension of a cup that uses least amount of paper

  • Thread starter disque
  • Start date
  • #1
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Homework Statement


A cone-shaped paper drinking cup is to be made to hold 30 cm3 of water. Find the height and radius of the cup that will use the smallest amount of paper.


Homework Equations


volume of a cone (1/3)(pi)(r^2)(h) = 30
SA of a cone pi(r)[sqrt(r^2 + h^2)]


The Attempt at a Solution


solve volume for h
plug h into SA
derive SA
calculate r
solve for h

I'm understanding how to do it, I just can't get the right answers.
 

Answers and Replies

  • #2
Pyrrhus
Homework Helper
2,178
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Show your work, so we can know where did you go wrong.
 
  • #3
29
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h = 90/(pir^2)

derivative of SA = 2pi*pir^2*r^2+90pi, denominator not needed, setting equal to zero.
 
  • #4
392
0


I got a different derivative (even after clearing out some denominators).
 

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