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If the sum of the surface areas of cube and a sphere is costnat, what is the ratio of an edge of the cube to the diameter of the sphere, when the sum of their volumes is minimum?

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PRADEEP PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE
  1. A point on the hypotenuse of a triangle is at distance a and b from th...

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

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

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

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

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

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

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  8. Find the rate of change of area of a square when its side is increasin...

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  9. If the rate of change of volume of a sphere is numerically equal to th...

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  10. If the area of a circle increases at a uniform rate, then prove that t...

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  11. Find a real number theta, 0 < theta < pi/2, which increases twice as f...

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  12. Find the rate of change of perimeter of a square when its side is incr...

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  13. Find the rate of change of perimeter of a square when its side is incr...

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  14. Find the rate of the change of surface area of a sphere when its radiu...

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  15. The volume of a cube is increasing at a constant rate. Prove that the ...

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  16. A particle is moving in a straight line such that its displacement s a...

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  17. The rate of change of the volume of a sphere w.r.t. its surface area, ...

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  18. Prove that the function f(x) = tanx-4x is strictly decreasing on (-pi/...

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  19. Find the interval in which the function f(X) = x^4 - (4x^3)/(3) is str...

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  20. Show that the function f given by f(x) = tan^-1(sinx+cosx), x>0 is alw...

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