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

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

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs)|34 Videos

  • APPLICATION OF DERIVATIVES

    OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs)|34 Videos

  • APPLICATION OF INTEGRALS

    OMEGA PUBLICATION|Exercise Multiple Choice Questions|16 Videos

Similar Questions

Explore conceptually related problems

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface area is cot^-1sqrt2

Show that the semi-vertical angle of the right-circular cone of maximum volume and of given slant height is cos^-1(1/sqrt3)

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.

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is tan^-1sqrt2 .

Show that the height of a closed right-circular cylinder of given volume and least surface area is equal to its diameter.

Show that the height of the cylinder, open at the top of given surface area and greatest volume is equal to the radius of its base.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 time the radius of the base.

Show that the right circular cone of least curved surface and given volume has an altitude equal to sqrt2 times the radius of the base.

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 .

OMEGA PUBLICATION-APPLICATION OF DERIVATIVES -Important Questions from (Miscellaneous Exercise )
  1. An open box with a square base is to be made out of a given iron sheet...

    Text Solution

    |

  2. Show that the height of the cylinder of maximum volume that can be ins...

    Text Solution

    |

  3. Show that semi-vertical angle of right circular cone of given surface ...

    Text Solution

    |

  4. Using differentials, find the approximate value of ((17)/(81))^(1//4)

    Text Solution

    |

  5. Find the intervals in which the function f given by f(x) = x^3 + (1/x^...

    Text Solution

    |

  6. Find the intervals in which the function f given by f(x) = x^3 + (1/x^...

    Text Solution

    |

  7. The length 'x' of a rectangle is decreasing at the rate of 5 cm per mi...

    Text Solution

    |

  8. The length 'x' of a rectangle is decreasing at the rate of 5 cm per mi...

    Text Solution

    |

  9. If the sum of the lengths of hypotenuse and a side of a right-angled t...

    Text Solution

    |

  10. Manufacturer can sell x items at a price of rupees Rs(5-(x/100)) each...

    Text Solution

    |

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

    Text Solution

    |

  12. A window has the shape of a rectangle surmounted by an equilateral tri...

    Text Solution

    |

  13. The volume of a cube is increasing at the rate of 8 cm^3/s. How fast i...

    Text Solution

    |

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

    Text Solution

    |

  15. The radius of a circle is increasing uniformly at the rate of 3 cm/s. ...

    Text Solution

    |

  16. Find the maximum profit that a company can make, if the profit functio...

    Text Solution

    |

  17. Find both the maximum value and the minimum value of 3x^4-8x^3+12x^2-4...

    Text Solution

    |

  18. Prove that the radius of the right-circlar cylinder of greatest curved...

    Text Solution

    |

  19. Find the equation of the normals to the curve y = x^3+2x+6 which are ...

    Text Solution

    |

  20. Find the equation of the tangent line to the curve y = x^2 - 2x + 7, w...

    Text Solution

    |