Home
Class 11
MATHS
Find the dimensions and the volume of th...

Find the dimensions and the volume of the greatest cylinder that can be inscribed in a sphere of radius a.

Text Solution

Verified by Experts

The correct Answer is:
height `= (2a)/(sqrt(3))`; radius `= (sqrt(2)a)/(sqrt(3))`; volume `= (4pi a^(3))/(3sqrt(3))` cubic units
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - I ) (STRAIGHT OBJECTIVE TYPE QUESTIONS)|74 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise LECTURE SHEET (EXERCISE - I ) (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS)|8 Videos

  • MAXIMA AND MINIMA

    AAKASH SERIES|Exercise Exercise - 8.2 (Long Answer Questions)|36 Videos

  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I (LEVEL-II (MORE THAN ONE CORRECT ANSWER TYPE QUESTIONS ) )|2 Videos

Similar Questions

Explore conceptually related problems

The volume of the largest cone that can be inscribed in a sphere of radius = 9cm is

The maximum volume of the right circular cone that can be inscribed in a sphere of radius R

The maximum area of the rectangle that can be inscribed in a circle of radius r is

The voluime of the largest possible right circular cylinder that can be in inscribed in a sphere of radius =sqrt(3) is

AAKASH SERIES-MAXIMA AND MINIMA -Advanced Subjective Type Questions
  1. Show that a conical tent of given capacity will require the least amou...

    Text Solution

    |

  2. The equation of the normal to the curve x^(2)=4y at (1,2) is

    Text Solution

    |

  3. Find the dimensions and the volume of the greatest cylinder that can b...

    Text Solution

    |

  4. Show that the altitude of the right circular cone of maximum volume th...

    Text Solution

    |

  5. Show that the semi-vertical angle of right circular cone of the maximu...

    Text Solution

    |

  6. Show that semi-vertical angle fo right circular cone of given surface ...

    Text Solution

    |

  7. A wire of length 'a' is cut into two parts which are bent in the form ...

    Text Solution

    |

  8. An open top box of maximum possible volume from a square piece of tin ...

    Text Solution

    |

  9. The point on the parabola y =x^(2) + 7x + 2 which is elosest to the li...

    Text Solution

    |

  10. A car starts from a point P at time t = 0 seconds and stops at point Q...

    Text Solution

    |

  11. A water tank has the shape of an inverted right circular cone with its...

    Text Solution

    |

  12. A tank with rectangular base and rectangular side, open at the top is ...

    Text Solution

    |

  13. If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x ...

    Text Solution

    |

  14. If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x ...

    Text Solution

    |

  15. If f(x) = {(3x^(2) + 12x - 1, -1 le x le 2),(" "37-x, 2 lt x ...

    Text Solution

    |

  16. Let f(x) = {(" "x e^(a x), x le 0),(x + a x^(2) - x^(3) , x ...

    Text Solution

    |

  17. Find the intervals in which f(x) = int(0)^(x){e^(t) - 1)(t+1)(t-2)(t+4...

    Text Solution

    |

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

    Text Solution

    |

  19. Let f, g, h be real valued functions defined on the interval [0, 1] by...

    Text Solution

    |

  20. Find the equation of tangents to the curve y = cos(x+y), -2pi le x le ...

    Text Solution

    |