sasogeek
  • sasogeek
A manufacturing company makes open cylindrical containers each with a capacity of 100cm^3. if the radius of the cylinders is r cm, find the value for which the area of the metal sheet required is minimum.
Mathematics
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sasogeek
  • sasogeek
A manufacturing company makes open cylindrical containers each with a capacity of 100cm^3. if the radius of the cylinders is r cm, find the value for which the area of the metal sheet required is minimum.
Mathematics
jamiebookeater
  • jamiebookeater
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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sasogeek
  • sasogeek
the capacity is 1000cm^3
sasogeek
  • sasogeek
typo
anonymous
  • anonymous
\(A = 2 \pi r h \) \[ V = \pi r^2 h = 10^3 \] substitute and then differentiate you will get your answer.

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sasogeek
  • sasogeek
how do i get rid of h...
anonymous
  • anonymous
I gave you so many hints .. :)
sasogeek
  • sasogeek
ok so \(\large h=\frac{10^3}{\pi r^2} \) i substitute this and then differentiate...
anonymous
  • anonymous
Seems good to me.
sasogeek
  • sasogeek
when i substitute, i end up with \(\large A=\frac{2000}{r} \) ... how do i differentiate this and still get a value of r ?

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