Home
Class 12
MATHS
The given quantity of metal is to be cos...

The given quantity of metal is to be cost into a half cylinder with a rectangular base and semicircular ends. Show that in order that the total surface area may be minimum, the ratio of the length of the cylinder to the diameter of its semi-circular ends is `pi:(pi+2)dot`

Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE -4 (LEVEL - I)|10 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 2 (LEVEL - II)|15 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

Similar Questions

Explore conceptually related problems

40.A given quantity of metal is to be cast into a half cylinder with a rectangular base and semicircular ends.Show that in order that the total surface area may be minimum,the ratio of the length of the cylinder to the diameter of its semi-circular ends is w'(

The total surface area of a solid right circular cylinder is twice that of a solid sphere. If they have the same radii, the ratio of the volume of the cylinder to that of the sphere is given by

The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2 . If the total surface area is 616 cm , what is the volume of the cylinder ?

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.

The curved surface area and the total surface area of a cylinder are in the ratio 1:2. If the total surface area of the right cylinder is 616 cm^(2) , then its volume is :

A right circular cylinder has a diameter of 20 cm and its curved surface area is 1000 cm^2 . What is the volume of the cylinder ?

A right circular cylinder is inscribed in a cone. show that the curved surface area of the cylinder is maximum when the diameter of the cylinder is equal to the radius of the base of the cone.

MOTION-MAXIMA AND MINIMA -EXERCISE - 3
  1. A trapezium ABCD is inscribed into a semicircle of radius l so that th...

    Text Solution

    |

  2. Find the locus of the foot of the perpendicular drawn from the cent...

    Text Solution

    |

  3. The given quantity of metal is to be cost into a half cylinder with a ...

    Text Solution

    |

  4. Determine A and B so that y = = A/x+ Bx has a minimum at the point (1,...

    Text Solution

    |

  5. Find the points of local maxima/minima of function f (x) = 2x^(3) -...

    Text Solution

    |

  6. Find the points of local maxima/minima of function f(x) = - (x - 1)^...

    Text Solution

    |

  7. Find the points of local maxima/minima of function f(x) = x ln x

    Text Solution

    |

  8. Let f(x) = {{:( 2 sin x ,, x gt 0) , ( x^(2) ,, x le 0):} . Investigat...

    Text Solution

    |

  9. Find the number of critical points of the function f (x) = - (3)/(4...

    Text Solution

    |

  10. Find the number of critical points of the function f(x) = |x - 2| +...

    Text Solution

    |

  11. Find the number of critical points of the function f (x) = min (tan...

    Text Solution

    |

  12. Let f (x) = x^(2) , x in [-1 , 2) Then show that f(x) has exactly one ...

    Text Solution

    |

  13. Let f (x) = x + sqrtx . Find the greatest and least value of f(x) for ...

    Text Solution

    |

  14. Let f(x) ={underset(x^(2) +nb " " x ge1)(3-x " "0le x lt1). Find ...

    Text Solution

    |

  15. Find the points of local maxima/minima of following functions (i) f ...

    Text Solution

    |

  16. Show that sin^(p) theta cos^(q) theta , p , q in N attains maximum val...

    Text Solution

    |

  17. A telephone company in a town has 500 subscribers on its list and c...

    Text Solution

    |

  18. A factory D is to be connected by a road with a straight railway line ...

    Text Solution

    |

  19. If y=(a x+b)/((x-1)(x-4)) has a turning value at (2,\ -1) find a\ &...

    Text Solution

    |

  20. A cubic function f(x) vanishes at x=-2 and has relative minimum/maximu...

    Text Solution

    |