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Show that semi-vertical angle of right ...

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is `sin^(-1)(1/3)`.

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A DAS GUPTA-Maxima and Minima-EXERCISE
  1. Find the maximum area of an isosceles triangle inscribed in the ellip...

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  2. Prove that the minimum length of the intercept made by the axes on the...

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  3. Show that semi-vertical angle of right circular cone of given surface...

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  4. Prove that a conical tent of given capacity will require the least ...

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  5. It is desired to construct a cylindrical vessel of capacity 500 cu m, ...

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

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  8. A box without lid having maximum volume is made out of square metal sh...

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

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  10. Show that the cone of the greatest volume which can be inscribed in a ...

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  11. Prove that the cone, circumscribing a sphere of radius r, has the mini...

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

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  13. A tree trunk I metres long, is in the shape of a frustum of a cone, th...

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  14. A swimmer S is in the sea at a distance dk m from the closest point A ...

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  15. A private telephone company serving a small community makes a profit o...

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  16. A factory D is to be connected by a road with a straight railway line ...

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  17. Fill in the blanks. f(x) =x^2 +ax^-1 will have a minimum at x=2 if a =

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  18. What is the area of the largest triangle that can be inscribed in a se...

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  19. x and y be two variables such that xgt0 and xy=1. Then the minimum val...

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  20. The value of a so that the sum of the squares of the roots of the equa...

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