Home
Class 12
MATHS
If a cone of maximum volume is inscri...

If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is `3//4` (b) `1//3` (c) `1//4` (d) `2//3`

A

`2/3`

B

`3/4`

C

`1/3`

D

`1/4`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise CRITICAL THINKING|129 Videos

  • APPICATIONS OF DEFINITE INTEGRAL

    TARGET PUBLICATION|Exercise EVALUATION TEST|18 Videos

  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 Videos

Similar Questions

Explore conceptually related problems

The height of the cone of maximum volume inscribed in a sphere of radius R is

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.

The ratio between the height of a right circular cone of maximum volume inscribed in given sphere and the diameter of the sphere is

A sphere of maximum volume is cut out from a solid hemisphere of radius r. The ratio of the volume of the hemisphere to that of the cut out sphere is: (a) 3:2 (b) 4:1 (c) 4:3 (d) 7:4

The radius of a sphere is equal to the radius of the base of a right circular cone,and the volume of the sphere is double the volume of the cone.The ratio of the height of the cone to the radius of its base is (a) 2:1quad (b) 1:2 (c) 2:3quad (d) 3:2

Show that the cone of greatest volume which can be inscribed in a given sphere is such that three times its altitude is twice the diameter of the sphere. Find the volume of the largest come inscribed ina sphere of radius R.

TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPETITIVE THINKING
  1. The height of the cylinder of the greatest volume that can be inscribe...

    Text Solution

    |

  2. The radius of the cylinder of maximum volume, which can be inscribed i...

    Text Solution

    |

  3. If a cone of maximum volume is inscribed in a given sphere, then th...

    Text Solution

    |

  4. Area of the greatest rectangle that can be inscribed in the ellipse x^...

    Text Solution

    |

  5. Suppose the cubic x^3-px+q has three real roots where pgt0 and qgt0 . ...

    Text Solution

    |

  6. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  7. Let f:""RvecR be defined by f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1} ....

    Text Solution

    |

  8. For x epsilon(0,(5pi)/2), definite f(x)=int(0)^(x)sqrt(t) sin t dt. T...

    Text Solution

    |

  9. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  10. If f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):} an...

    Text Solution

    |

  11. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  12. Let f(x)=(1+b^(2))x^(2)+2bx+1 and let m(b) be the minimum value of f ...

    Text Solution

    |

  13. Given P(x) =x^(4) +ax^(3) +bx^(2) +cx +d such that x=0 is the only re...

    Text Solution

    |

  14. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  15. The points on the curve y=12x-x^3 at which the gradient is zero are

    Text Solution

    |

  16. The displacement of a particle at time t is x, where x=t^4-kt^3. IF th...

    Text Solution

    |

  17. If f(x) satifies of conditiohns of Rolle's theorem in [1,2] and f(x) i...

    Text Solution

    |

  18. IF f(x)=x,-1lexle1, then function f(x) is

    Text Solution

    |

  19. If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...

    Text Solution

    |

  20. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |