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Show that a cylinder of given volume, op...

Show that a cylinder of given volume, open at the top, has minimum total surface area if its height is equal to radius of the base.

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. Find the area of the largest isosceles triangle having perimeter 18 me...

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  2. A wire 10 meter long is cut into two parts. One part is bent into the ...

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  3. Show that a cylinder of given volume, open at the top, has minimum tot...

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  4. Find the altitude of the circular cylinder of maximum volume that can ...

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  5. Find the altitude of the circular cone of maximum volume that can be i...

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  6. Show that the semi-vertical angle of the right-circular cone of maximu...

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  7. The combined resistance of two resistors R1 and R@ (R1,R2>0) is given ...

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  8. Show that height of the cylinder of greatest volume which can be inscr...

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

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  10. A metal box with a square box and vertical sides is to contain 512 c^3...

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  11. An isosceles triangle of vertical angle 2theta is inscribed in a circl...

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  12. If the sum of the lengths of hypotenuse and a side of a right-angled t...

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

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  14. A point on the hypotenuse of a triangle is at distance a and b from th...

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  15. Find the dimensions of the rectangle of perimeter 36 cm which will swe...

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  16. If the sum of the surface areas of cube and a sphere is costnat, what ...

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  17. If the length of three sides of a trapezium other than base are equal ...

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  18. Find the shortest distance of the point (0, c) from the parabola y = x...

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  19. Let AP and BQ be two vertical poles at points A and B respectively. If...

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  20. A window has the shape of a rectangle surmounted by an equilateral tri...

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