Home
Class 12
MATHS
An open box with a square base is to ...

An open box with a square base is to be made out of a given quantity of card board of area c2 square units. Show that the maximum volume of the box is `(c^3)/(6sqrt(3))` cubic units.

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE 1 (f) (Long Answer Type Questions (II))|33 Videos
  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise Objective Type Questions (A. Multiple Choice Questions)|45 Videos
  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE 1 (e) (Long Answer Type Questions (I))|32 Videos
  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

An open box with a square base is to be made out of a given quantity of card board of area c^(2) square units.Show that the maximum volume of the box is (c^(3))/(6sqrt(3)) cubic units.

An open box with a square base is to be made out of a given quantity of cardboard of area c^(2) show that the maximum volume of box is (c^(3))/(6sqrt(3))

An open box,with a square base,is to be made out of a given quantity of metal sheet of area C^(2). show that the maximum volume of the box is (C^(3))/(6sqrt(3))

The areas of the three adjacent faces of a cuboidal box are x, 4x and 9x square unit. What is the volume of the box?

An open box is to be made out of a piece of a square card board of sides 18 cm by cutting off equal squares from the corners and turning up the sides. Find the maximum volume of the box.

A box with a square base is to have an open top. The surface area of the box is 192sq.cm. What should be its dimensions in order that the volume is largest?

The edges of a rectangular box are in the ratio 1:2:3 and area of its floor is 8 cm^(2) . The volume of the box is

A box is made with square base and open top. The area ofthe material used is 192sq.cms. If the volume of the box is maximum,the dimensions of the box are

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 1 (f) (Long Answer Type Questions (I))
  1. Find two positive numbers x and y such that their sum is 35 and the ...

    Text Solution

    |

  2. Find two positive numbers whose sum is 16 and the sum of whose cube...

    Text Solution

    |

  3. Find two positive numbers x and y such that x + y = 60and x y^3is max...

    Text Solution

    |

  4. How should we choose two numbers, each greater than or equal to -2 ...

    Text Solution

    |

  5. Find the maximum slope of the curve y=-x^3+3x^2+2x-27 .

    Text Solution

    |

  6. Two sides of a triangle are given. The angle between them such that th...

    Text Solution

    |

  7. A wire of length 36m is to be cut into two pieces. One of the piece...

    Text Solution

    |

  8. A wire of length 36cm is cut into the two pieces, one of the pieces is...

    Text Solution

    |

  9. Prove that the perimeter of a right - angled triangle of given hypoten...

    Text Solution

    |

  10. Prove that the area of right-angled triangle of given hypotenuse is...

    Text Solution

    |

  11. Prove that the least perimeter of an isosceles triangle in which a cir...

    Text Solution

    |

  12. Show that of all the rectangles of given area, the square has the s...

    Text Solution

    |

  13. Show that the rectangle of maximum perimeter which can be inscribed...

    Text Solution

    |

  14. Show that the rectangle of maximum area that can be inscribed in a ...

    Text Solution

    |

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

    Text Solution

    |

  16. A rectangle is inscribed in a semi-circle of radius r with one of its ...

    Text Solution

    |

  17. Of all rectangles, each of which has perimeter : (i) 40 cm (ii) 60...

    Text Solution

    |

  18. An open box with a square base is to be made out of a given quantit...

    Text Solution

    |

  19. Show that the semi - vertical angle of the right - circular cone of ma...

    Text Solution

    |

  20. Prove that the semi-vertical angle of the right circular cone of given...

    Text Solution

    |