Home
Class 12
MATHS
Show that the altitude of the right circ...

Show that the altitude of the right circulau cone of maximum volume that can be inscribed in a sphere of radius r is `(4r) /(3) `. also show that the maximum volume of cone is `(8)/(27)` of the volume of the sphere.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise Objective Type Questions (A. Multiple Choice Questions)|45 Videos

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise Objective Type Questions (B. Fill in the Blanks)|10 Videos

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE 1 (f) (Long Answer Type Questions (I))|24 Videos

  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/(3) .

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius R is (4R)/(3) .

Show that the altitude of a right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3..

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4R)/(3) .Also find maximum volume in terms of volume of the sphere.

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

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

Show that the radius of right - circular cylinder of maximum volume, that can be inscribed in a sphere of radius 18 cm, is 6sqrt6cm .

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 1 (f) (Long Answer Type Questions (II))
  1. Show that the volume of the greatest cylinder, which can be inscribed ...

    Text Solution

    |

  2. Show that the altitude of the right circulau cone of maximum volume th...

    Text Solution

    |

  3. Find the volume of the larges cylinder that can be inscribed in a s...

    Text Solution

    |

  4. Find the volume of the larges cylinder that can be inscribed in a s...

    Text Solution

    |

  5. Show that the right-circular cone of least curved surface and given...

    Text Solution

    |

  6. Show that the height of the cylinder of maximum volume that can be in...

    Text Solution

    |

  7. Find the height of right circular cylinder of maximum volume that can ...

    Text Solution

    |

  8. Show that the radius of right - circular cylinder of maximum volume, t...

    Text Solution

    |

  9. Prove that the radius of the right circular cylinder of greatest cu...

    Text Solution

    |

  10. Of all the closed cylinderical cans (right - circular), which enclose ...

    Text Solution

    |

  11. Show that the surface area of a closed cuboid with square base and ...

    Text Solution

    |

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

    Text Solution

    |

  13. A window is the in the form of a reactangle, surmounted by a semi - ci...

    Text Solution

    |

  14. Show that a cylinder of a given volume which is open at the top has...

    Text Solution

    |

  15. The height of a closed cylinder of given volume and the minimum sur...

    Text Solution

    |

  16. Rectangles are inscribed inside a semicircle of radius r. Find the r...

    Text Solution

    |

  17. A square-based tank of capacity 250 cu m has to bedug out. The cost of...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. An open box is to be made of square sheet of tin with side 20 cm, by c...

    Text Solution

    |