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Can Design

  • There are many factors to consider in food packaging, including marketing, durability, cost and materials. In this problem we minimize the cost of materials for a can.
    Find the height and radius that minimizes the surface area of a can whose volume is 1 liter = 1000 cm^{3}


    r, h are:

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Solving an Optimization Problem using Implicit Differen­tiation ▼Math Symbols ▲Math Symbols

Common forms and functions
  • x+y x+y
  • x·yx*y
  • x/yx÷y
  • xyx**y
  • √xsqrt(x)
  • x!factorial(x)
  • ln(x)log(x)
  • exexp(x)
  • log10(x)log(x, 10)
  • log2(x)log(x, 2)
  • sin(x)sin(x)
  • cos(x)cos(x)
  • tan(x)tan(x)
  • cot(x)1/tan(x)
  • atan(x)atan(x)
  • asin(x)asin(x)
  • acos(x)acos(x)
  • sinh(x)sinh(x)
  • cosh(x)cosh(x)
  • tanh(x)tanh(x)
  • eE
  • πpi

Suppose you wish to build a grain silo with volume V made up of a steel cylinder and a hemispherical roof. The steel sheets covering the surface of the silo are quite expensive, so you wish to minimize the surface area of your silo.What height and radius should the silo have for a given volume V ?

Although it is possible to solve this problem by the same method used in the can design question, it turns out to be much simpler to use implicit differentiation to find \frac{d}{dr}

Answer this question for:
  • A silo with a circular floor (to keep out gophers) 

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Solving an Optimization Problem using Implicit Differen­tiation

Suppose you wish to build a grain silo with volume V made up of a steel cylinder and a hemispherical roof. The steel sheets covering the surface of the silo are quite expensive, so you wish to minimize the surface area of your silo.What height and radius should the silo have for a given volume V ?

Although it is possible to solve this problem by the same method used in the can design question, it turns out to be much simpler to use implicit differentiation to find \frac{d}{dr}

Answer this question for:
  • A silo with no built-in flooring (for use in regions with no gophers). h equals to:

Please to take this test and advance your course progress

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Massachusetts Institute Of Technology
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Lecture 12: Related rates

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