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Prove that the volume of the largest con...

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is `(8)/(27)` of the volume of the sphere.

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`(8)/(27)`
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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -EXERCISE - 6.5
  1. What is the maximum value of the function sin x + cos x ?

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  2. Find the maximum value of 2x^(3)-24x+107 in the interval [1, 3]. Find ...

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  3. It is given that at x = 1, the function x^(4)-62x^(2)+ax+9 attains its...

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  4. Find the maximum and minimum values of x+sin(2x) on [0, 2pi].

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  5. Find two numbers whose sum is 24 and whose product is as large as poss...

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  6. Find two positive numbers x and y such that x+y=60 and xy^(3) is maxim...

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  7. Find two positive numbers x and y such that their sum is 35 and the pr...

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  8. Find two positive numbers whose sum is 16 and the sum of whose cubes i...

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  9. A square piece of tin of side 18 cm is to be made into a box without t...

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

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  11. Show that of all rectangles inscribed in a given fixed circle, the squ...

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  12. Show that the right circular cylinder of given surface and maximum vol...

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  13. Of all the closed cylindrical cans (right circular), of a given volume...

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  14. A wire of length 28 m, is to be cut into two pieces. One of the pieces...

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  15. Prove that the volume of the largest cone that can be inscribed in a s...

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

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  17. Show that the semi-vertical angle of the cone of the maximum volume an...

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  18. Show that semi - vertical angle of right circular cone of given surfac...

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  19. The point on the curve x^(2)=2y which is nearest to the point (0, 5) i...

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  20. For all real values of x, the minimum value of f(x)=(1-x+x^(2))/(1+x+x...

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