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

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 pi h^3 tan^2 alpha`

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE (Multiple choice questions)|3 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (SECTION VI)|9 Videos

  • APPLICATION OF INTEGRALS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE|36 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)|94 Videos

Similar Questions

Explore conceptually related problems

Show that the 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 greatest volume of cylinder is 4/27pi h^3tan^2 alpha

Show that the height of the circular cylinder of maximum volume that can be inscribed in a given right-circular cone of height h is 1/3 h

Show that the volume of the greatest cylinder, which can be inscribed in a cone of 4 height 'h' and semi-vertical angle 30° is 4/81 pi h^3 .

Show that the volume of the greatest cylinder, which can be inscribed in a cone of height 'h' and semi-vertical angle 30^@ is 4/(81) pi h^3

Show that the volume of the greatest cylinder, which can be inscribed in a cone of 4 height 'h' and semi-vertical angle theta is 4/27 pi h^3 tan^2 theta .

Find the height of a right circular cylinder of maximum volume, which can be inscribed in a sphere of radius 9 cm.

Find the height of a right circular cylinder of maximum volume, which can be inscribed in a sphere of radius 8 cm .

Find the height of a-right circular cylinder of maximum volume, which can be inscribed in a sphere of radius 10 cm.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R/sqrt3 . Also find the maximum volume.

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

BETTER CHOICE PUBLICATION-APPLICATIONS OF DERIVATIVES-ASSIGNMENT (SECTION VII) (Long Answer Type Questions)
  1. Find two positive numbers whose sum is 32 and product is large as poss...

    Text Solution

    |

  2. Find two numbers x and y such that x+y=15andx^(2)y^(3) is maximum.

    Text Solution

    |

  3. Find two positive numbers whose sum is 24 and their sum of squares is ...

    Text Solution

    |

  4. Find two positive numbers x and y such that x+y=36andxy^(3) is maximum...

    Text Solution

    |

  5. Find two positive numbers whose sum is 14 and sum of squares is minimu...

    Text Solution

    |

  6. Find the area of the largest rectangle having the perimeter 200 cm.

    Text Solution

    |

  7. Find the rate of change of the area of a circle with respect to its ra...

    Text Solution

    |

  8. Find the point on the curve x^(2)=8y which is nearest to the point (2,...

    Text Solution

    |

  9. A figure consists of a semi-circle with a rectangle on its diameter. G...

    Text Solution

    |

  10. A window consists if a semi-circle with a rectangel on its diameter. I...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Find two positive numbers whose sum is 14 and their sum of squares is ...

    Text Solution

    |

  14. Show that the height of the cylinder, open at the top of given surface...

    Text Solution

    |

  15. Find the rate of change of the area of the circle with respect to its ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. The radius of the circle is increasing at the rate of 0.7 cm/s . What ...

    Text Solution

    |

  19. A balloon which always remain spherical has a variable radius. Find th...

    Text Solution

    |