Home
Class 12
MATHS
Prove that the radius of the right circu...

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.

Text Solution

Verified by Experts

OE=x
OC=r
AO=h
`/_ AOC cong /_ QEC`
`(AO)/(OC)=(QE)/(EC)`
`(QE)=(AO)/(OC)(EC)`
=`h/r(r-x)`
`deltax=2pix(h/r(r-x))`
...
Promotional Banner

Topper's Solved these Questions

  • CUET MOCK TEST 2022

    XII BOARDS PREVIOUS YEAR|Exercise Question|49 Videos

Similar Questions

Explore conceptually related problems

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

A right circular cone of height 4cm has a curved surface area 47.1cm^(2)

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 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)pi h^(3)tan^(2)alpha

Curved (Lateral) Surface area of Right Circular Cylinder

Prove that the cylinder inscribed in a right circular cone has maximum curved surface area if the radius of cylinder is half the radius of cone.

XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Evaluate : int xsin^(-1)\ x\ \ dx

    Text Solution

    |

  2. Evaluate : int(dx)/(sqrt(5-4x-2x^2))

    Text Solution

    |

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

    Text Solution

    |

  4. The amount of pollution content added in air in a city due to x- diese...

    Text Solution

    |

  5. An open box with a square base is to be made out of a given quantit...

    Text Solution

    |

  6. Solve the following differential equation: (dy)/(dx)+ycotx=4x\ cos e c...

    Text Solution

    |

  7. Find the particular solution of the differential equation: (1+e^(2x))d...

    Text Solution

    |

  8. Let vec a= hat i+4 hat j+2 hat k ,\ \ vec b=3 hat i-\ 2 hat j+7 hat ...

    Text Solution

    |

  9. If vec a= hat i+ hat j+ hat k ,\ \ vec b=4 hat i-\ 2 hat j+3 hat k a...

    Text Solution

    |

  10. Prove, using properties of determinants: |[y+k, y, y],[ y, y+k, y],[...

    Text Solution

    |

  11. Consider f: R+ rarr [4, oo] given by f(x)=x^2+4. Show that f is inv...

    Text Solution

    |

  12. What are the direction cosines of a line, which makes equal angles ...

    Text Solution

    |

  13. Evaluate: int(dx)/(x(x^5+3))

    Text Solution

    |

  14. Find the value of k so that the function f defined by f(x)={(kcosx)/(...

    Text Solution

    |

  15. Prove that : tan^(-1)(1/2)+tan^(-1)(1/5)+tan^(-1)(1/8)=pi/4dot

    Text Solution

    |

  16. Find the vector and cartesian equations of the line passing through...

    Text Solution

    |

  17. Evaluate: |(cos15^0,sin15^0),(sin75^0,cos75^0)|

    Text Solution

    |

  18. What is the principal value of cos^(-1)cos((2pi)/3)+sin^(-1)sin((2p...

    Text Solution

    |

  19. Let A = {1, 2, 3}, B = {4, 5, 6, 7}and let f = {(1, 4), (2, 5), (3, 6)...

    Text Solution

    |

  20. Evaluate: int0^4(|x|+|x-2|+|x-4|)\ dx

    Text Solution

    |