Home
Class 12
MATHS
Show that semi - vertical angle of right...

Show that semi - vertical angle of right circular cone of given surface area and maximum volume is `sin^(-1)((1)/(3))`.

Text Solution

Verified by Experts

The correct Answer is:
`alpha = sin^(-1)((1)/(3))`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise MISCELANEOUS EXERCISE - 6|27 Videos
  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|85 Videos
  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise EXERCISE - 6.4|23 Videos
  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos
  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^(-1)sqrt(2) .

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

Find the volume of right circular cone with radius 6 cm and height 7 cm.

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 right circular cone of least curved surface and given volume has an altitude equal to sqrt(2) time the radius of the base.

The radius of sphere is 3.5 cm Find its surface area and volume .

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 (4pi)/(27)h^(3) tan^(2)alpha .

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

Find the curved surface area of a right circular cone whose slant height is 10 cm and base radius is 7 cm.

Show that the angle between the diagonal of a cube is cos^(-1)((1)/(3)) .

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -EXERCISE - 6.5
  1. What is the maximum value of the function sin x + cos x ?

    Text Solution

    |

  2. Find the maximum value of 2x^(3)-24x+107 in the interval [1, 3]. Find ...

    Text Solution

    |

  3. It is given that at x = 1, the function x^(4)-62x^(2)+ax+9 attains its...

    Text Solution

    |

  4. Find the maximum and minimum values of x+sin(2x) on [0, 2pi].

    Text Solution

    |

  5. Find two numbers whose sum is 24 and whose product is as large as poss...

    Text Solution

    |

  6. Find two positive numbers x and y such that x+y=60 and xy^(3) is maxim...

    Text Solution

    |

  7. Find two positive numbers x and y such that their sum is 35 and the pr...

    Text Solution

    |

  8. Find two positive numbers whose sum is 16 and the sum of whose cubes i...

    Text Solution

    |

  9. A square piece of tin of side 18 cm is to be made into a box without t...

    Text Solution

    |

  10. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wit...

    Text Solution

    |

  11. Show that of all rectangles inscribed in a given fixed circle, the squ...

    Text Solution

    |

  12. Show that the right circular cylinder of given surface and maximum vol...

    Text Solution

    |

  13. Of all the closed cylindrical cans (right circular), of a given volume...

    Text Solution

    |

  14. A wire of length 28 m, is to be cut into two pieces. One of the pieces...

    Text Solution

    |

  15. Prove that the volume of the largest cone that can be inscribed in a s...

    Text Solution

    |

  16. Show that the right circular cone of least curved surface and given vo...

    Text Solution

    |

  17. Show that the semi-vertical angle of the cone of the maximum volume an...

    Text Solution

    |

  18. Show that semi - vertical angle of right circular cone of given surfac...

    Text Solution

    |

  19. The point on the curve x^(2)=2y which is nearest to the point (0, 5) i...

    Text Solution

    |

  20. For all real values of x, the minimum value of f(x)=(1-x+x^(2))/(1+x+x...

    Text Solution

    |