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

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`

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

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

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

If S denotes the area of the curved surface of a right circular cone of height h and semivertical angle alpha then S equals___

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.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. There is a point (p,q) on the graph of f(x)=x^(2) and a point (r,s) on...

    Text Solution

    |

  2. Prove theat the tangent drawn at any point to the curve f(x)=x^(5)+3x^...

    Text Solution

    |

  3. Show that height of the cylinder of greatest volume which can be ins...

    Text Solution

    |

  4. A curve is defined parametrically by the the equation x=t^(2) and y=t^...

    Text Solution

    |

  5. The equation of the tangent to the curve y={(x^2sin"1/x,xne0),(0,x=0):...

    Text Solution

    |

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

    Text Solution

    |

  7. Statement 1: If f(x) is differentiable in [0,1] such that f(0)=f(...

    Text Solution

    |

  8. Find the equation of tangent to the curve y=sin^(-1)((2x)/(1+x^2)) a t...

    Text Solution

    |

  9. The lateral surface area of a cube is 169sq.cm., then the volume of th...

    Text Solution

    |

  10. Consider the polynomial function f(x)=x^7/7-x^6/6+x^5/5-x^4/4+x^3/3-x^...

    Text Solution

    |

  11. Find the equations of the normal to the curve y=x^3+2x+6 which are par...

    Text Solution

    |

  12. A sheet of area 40m^2 is used to make an open tank with square base. F...

    Text Solution

    |

  13. Let y=f(x) be a polynomial of odd degree (geq3) with real coefficients...

    Text Solution

    |

  14. Find the equation of tangent and normal to the curve x=(2a t^2)/((1+t^...

    Text Solution

    |

  15. Find the points on the curve 5x^2-8x y+5y^2=4 whose distance from the ...

    Text Solution

    |

  16. If d is the minimum distance between the curves f(x)=e^x a n dg(x)=(l...

    Text Solution

    |

  17. L L ' is the latus rectum of the parabola y^2= 4ax and PP' is a doubl...

    Text Solution

    |

  18. Let f(x0 be a non-constant thrice differentiable function defined on (...

    Text Solution

    |

  19. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |

  20. Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an...

    Text Solution

    |