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Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is `2R/sqrt3`. Also find the maximum volume.

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MODERN PUBLICATION-APPLICATION OF DERIVATIVES-EXERCISE
  1. Prove that volume of largest cone, which can be inscribed in a sphere,...

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  2. Show that the right circular cone of least curved surface and given vo...

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  3. Show that the height of the cylinder of maximum volume that can be ins...

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  4. Show that the radius of right circular cylinder of maximum volume, tha...

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  5. Prove that the radius of the right-circlar cylinder of greatest curved...

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  6. Of all the closed cylindrical cans (right-circular). Which enclose a g...

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  7. Show that the surface area of a closed cuboid with surface base and gi...

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  8. A figure consists of a semi-circle with a rectangle on its diameter. G...

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  9. A window is in the form of a rectangle surmounted by a semi-circular o...

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  10. A window consists if a semi-circle with a rectangel on its diameter. I...

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  11. Show that the height of the cylinder, open at the top of given surface...

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  12. Show that the height of the cylinder, open at the top of given surface...

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  13. Show that the height of a closed right-circular cylinder of given volu...

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  14. Given the sum of the perimiter of a square and a circle, show that the...

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  15. A square piece of tin of side 24 cm is to be made into a box without t...

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  16. A square-based tank of capacity 250 cu m has to bedug out. The cost of...

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  17. A tank with rectangular base and rectangular sides, open at the top is...

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  18. A rectangular sheet of tin 45 cm x 24 cm is to be made into a box with...

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  19. An open box with a square base is to be made out of a given iron sheet...

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  20. A farmer wants to construct a circular well and a square garden in his...

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