Home
Class 12
MATHS
Show that height of the cylinder of g...

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle is one-third that of the cone and the greatest volume of cylinder is `4/(27)pih^3tan^2alphadot`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT BANGLISH|Exercise EXERCISE 6.5|48 Videos

  • APPLICATION OF INTEGRALS

    NCERT BANGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi vertical angle alpha is one-third that of the cone and the greatest volume of cylinder is 4/(27)pih^3tan^2alphadot

Find the cylinder of maximum volume which can be inscribed in a cone of height h and semivertical angle alpha .

The height of the cylinder of maximum volume that can be inscribed in a sphere of radius a, is-

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3))

The height of a right circular cone is 40 cm and semi-vertical angle is 30^@ , the slant height of the cone is =?

Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm .

Prove that the radius of the right circular cylinder of greatest curved surface which can be inscribed in a given cone is half that of the cone.

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

NCERT BANGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.6
  1. Show that the normal at any point θ to the curve x = a costheta + a th...

    Text Solution

    |

  2. Find the intervals in which the function f given by f(x)=(4sinx-2x-xc...

    Text Solution

    |

  3. Find the intervals in which the function f given by f(x) =x^(3) +(1)/(...

    Text Solution

    |

  4. Find the maximum area of an isosceles triangle inscribed in the ellips...

    Text Solution

    |

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

    Text Solution

    |

  6. The sum of the perimeter of a circle and square is k, where k is some ...

    Text Solution

    |

  7. A window is in the form of a rectangle surmounted by a semicircular...

    Text Solution

    |

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

    Text Solution

    |

  9. Find the points at which the function f given by f (x) = (x-2)^(4)(x+1...

    Text Solution

    |

  10. Find the absolute maximum and minimum values of the function f given b...

    Text Solution

    |

  11. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  12. Let f be a function defined on [a, b] such that f ′(x) gt 0, for all x...

    Text Solution

    |

  13. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  14. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  15. A cylindrical tank of radius 10 m is being filled with wheat at the ra...

    Text Solution

    |

  16. The slope of the tangent to the curve x=t^(2)+3t-8,y=2t^(2)-2t-5 at th...

    Text Solution

    |

  17. The line y = mx + 1 is a tangent to the curve y^(2)= 4x if the value o...

    Text Solution

    |

  18. The normal at the point (1,1) on the curve 2y + x^(2) = 3 is

    Text Solution

    |

  19. The normal to the curve x^(2) = 4y passing (1,2) is

    Text Solution

    |

  20. The points on the curve 9y^(2) = x^(3) , where the normal to the curve...

    Text Solution

    |