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`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    RD SHARMA ENGLISH|Exercise All Questions|144 Videos
  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA ENGLISH|Exercise All Questions|125 Videos

Similar Questions

Explore conceptually related problems

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.

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.

Show that the height of a cone of maximum volume inscribed in a sphare has the ration with the radius of sphere as 4 : 3 .

A right circular cone whose base radius is 4 is inscribed in a sphere of radius 5. what is the ratio of the volume of the cone to the volume of the sphere?

A cone is inscribed in a sphere of radius 12 cm. If the volume of the cone is maximum, find its height.

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

A cone and a sphere have equal radii and equal volumes. Find the ratio of the diameter of the sphere to the height of the cone.

A cone of height 4 cm is melted and recast into a sphere of diameter 8 cm .Find the radius of the base of the cone.

The volume of a sphere is (4pi)/(3) cm^(3) .Find the volume of that cube whose edge is equal to the diameter of the sphere.

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is (a) 3:5 (b) 2:5 (c) 3:1 (d) 1:3

RD SHARMA ENGLISH-MAXIMA AND MINIMA-All Questions
  1. The function f(x)=sum(r=1)^5(x-r)^2 assuming minimum value at x= ...

    Text Solution

    |

  2. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (...

    Text Solution

    |

  3. If x lies in the interval [0,\ 1] , then the least value of x^2+x+1...

    Text Solution

    |

  4. The least value of the function f(x)=x^3-18 x^2+96 x in the interval [...

    Text Solution

    |

  5. The maximum value of f(x)=x/(4+x+x^2) on [-1,1] is (a)1/4 (b) -1/3 (c)...

    Text Solution

    |

  6. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

    Text Solution

    |

  7. If x+y=8 , then the maximum value of x y is (a) 8 (b) 16 (c) 20 (d)...

    Text Solution

    |

  8. The least and greatest values of f(x)=x^3-6x^2+9x in [0,\ 6] , are ...

    Text Solution

    |

  9. f(x)=sin+sqrt(3)cosx is maximum when x= pi/3 (b) pi/4 (c) pi/6 (d) 0

    Text Solution

    |

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

    Text Solution

    |

  11. The minimum value of (x^2+(250)/x) is (a) 75 (b) 50 (c) 25 (d) 55

    Text Solution

    |

  12. If f(x)=x+1/x ,\ \ x >0 , then its greatest value is -2 (b) 0 (c) 3...

    Text Solution

    |

  13. If f(x)=1/(4x^2+2x+1) , then its maximum value is 4/3 (b) 2/3 (c) 1...

    Text Solution

    |

  14. Let x ,\ y be two variables and x >0,\ \ x y=1 , then minimum value of...

    Text Solution

    |

  15. f(x)=1+2sinx+3cos^2x ,\ 0lt=xlt=(2pi)/3 is (a)Minimum at x=pi//2 (b) M...

    Text Solution

    |

  16. The function f(x)=2x^3-15 x^2+36 x+4 is maximum at x= (a) 3 (b) 0 (c)...

    Text Solution

    |

  17. The maximum value of f(x)=x/(4-x+x^2) on [-1,1] is (a)1/4 (b) -1/3 (c)...

    Text Solution

    |

  18. Let f(x)=2x^3-3x^2-12 x+5 on [-2,\ 4] . The relative maximum occurs...

    Text Solution

    |

  19. The minimum value of x\ (log)e x is equal to e (b) 1//e (c) -1//e (d) ...

    Text Solution

    |

  20. The minimum value of the function f(x)=2x^3-21 x^2+36 x-20 is -128 ...

    Text Solution

    |