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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)/(sqrt(3))`. Also find the maximum volume.

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The correct Answer is:
`(4piR^(3))/(3sqrt3)" cube units"`
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MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 1 (f) (Long Answer Type Questions (II))
  1. Find the volume of the larges cylinder that can be inscribed in a s...

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

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

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  4. Find the height of right circular cylinder of maximum volume that can ...

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  5. Show that the radius of right - circular cylinder of maximum volume, t...

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  6. Prove that the radius of the right circular cylinder of greatest cu...

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  7. Of all the closed cylinderical cans (right - circular), which enclose ...

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  8. Show that the surface area of a closed cuboid with square base and ...

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  10. A window is the in the form of a reactangle, surmounted by a semi - ci...

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  11. Show that a cylinder of a given volume which is open at the top has...

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  12. The height of a closed cylinder of given volume and the minimum sur...

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  13. Rectangles are inscribed inside a semicircle of radius r. Find the r...

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

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

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  16. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box ...

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  17. An open box is to be made of square sheet of tin with side 20 cm, by c...

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  18. A canon is fired at an angle theta(0le theta le(pi)/(2)) with the hori...

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  19. Find the maximum profit that a company can make, if the profit functi...

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  20. Find the maximum profit that a company can make, if the profit functio...

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