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

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MODEL TEST PAPER - 7

    ICSE|Exercise Section - B (In sub-parts (i) and (ii) choose the correct option and in sub-parts (iii) to (v), answer the questions as instructed.) |5 Videos
  • MODEL TEST PAPER - 7

    ICSE|Exercise Section - B|5 Videos
  • MODEL TEST PAPER - 7

    ICSE|Exercise Section - C |5 Videos
  • MODEL TEST PAPER - 4

    ICSE|Exercise SECTION - C|10 Videos
  • MODEL TEST PAPER - 8

    ICSE|Exercise Section - C |6 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) .

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is cot^(-1)(sqrt(2))dot

Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is cot^(-1)(sqrt(2))dot

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

Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is 1/3h

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 .

The total surface area of a cone whose radius is (r)/(2) and slant height 2l is

The semi-vertical angle of a cone remains constant. If its height increases by 2%, then find the approximate increase in its volume.

Show that the semi vertical angle of a right circular cone of given total surface area and max volume is sin^-1 (1/3)

Show that the height of the right circular cone of maximum volume that can be inscribed in a sphere of radius 12 cm is 16 cm.

ICSE-MODEL TEST PAPER - 7-Section - A
  1. Using L' Hospital' s rule prove that lim(x to (pi)/(2)) (sec x - tan x...

    Text Solution

    |

  2. Show that the function f (x)={ {:(3x^(2) + 12 x - 1,- 1 le x le 2 )...

    Text Solution

    |

  3. Solve : cos ^(-1) x + sin ^(-1) "" (x)/( 2) = (pi)/(6)

    Text Solution

    |

  4. If x^(y) * y^(x) = (x + y) ^(5) , " find " (dy)/( dx)

    Text Solution

    |

  5. Evaluate : int (1) ^(e) ( dx)/( x (1 + log x))

    Text Solution

    |

  6. Evaluate int tan ^(2) x sec^(4) x dx

    Text Solution

    |

  7. Solve : y - x (dy)/( dx) = 2 (1 + x^(2)"" (dy)/( dx))

    Text Solution

    |

  8. Show that the function f : R to defined by f (x) = x^(3) + 3 is inver...

    Text Solution

    |

  9. Find the probability distribution of the number of green balls drawn w...

    Text Solution

    |

  10. Evaluate : int (sqrt(x^(2) + 1) ( log (x^(2) + 1) - 2 log x))/( x^(4))...

    Text Solution

    |

  11. Evaluate : int (-1) ^(1) e^(x) dx .

    Text Solution

    |

  12. If y = tan ^(-1) (sec x + tan x) , " find " (d^(2) y)/( dx^(2)) at x...

    Text Solution

    |

  13. Find the derivative of tan^(-1) "" (sqrt(1 + x^(2)) - 1)/( x) with res...

    Text Solution

    |

  14. Using properties of determinants, prove that |{:(y + z ,z + x ,x + ...

    Text Solution

    |

  15. Show that the homogenous system of equations x - 2y + z = 0, x + y -...

    Text Solution

    |

  16. Show that semi-vertical angle of a cone of maximum volume and given sl...

    Text Solution

    |

  17. Show that the isosceles triangle of maximum area that can be inscribed...

    Text Solution

    |

  18. Evaluate : int (dx)/( (1 - x^(2)) sqrt( 1 + x^(2)))

    Text Solution

    |

  19. You note that your officer is happy with 60% of your calls, so, you as...

    Text Solution

    |