Home
Class 12
MATHS
A rectangular sheet of tin 45 cm by 2...

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?

Text Solution

Verified by Experts

The correct Answer is:
5 cm
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

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

    MODERN PUBLICATION|Exercise Objective Type Questions (B. Fill in the Blanks)|10 Videos
  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE 1 (f) (Long Answer Type Questions (I))|24 Videos
  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

A rectangular sheet of tin 45cm by 24cm is to be made into a box without top,by cutting off squares from each corners and folding up the flaps.What should be the side of the square to be cut off so that the volume of the box is maximum possible?

A rectangular sheet of tin 45cm by 24cm is to be made into a box without top,by cutting off square from each corner and folding up the flaps.What should be the side of the square to be cut off so that the volume of the box is maximum?

A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from each corner and foding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum ? Also, find this maximum volume.

A square piece of tin of side 18cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box.What should be the side of the square to be cut off so that the volume of the box is maximum? Also,find the maximum volume.

A square piece of tin of side 24 cm is to be made into a box without top by cutting a square from each and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum ? Also, find the maximum volume.

A square piece of tin of side 18cm is to be made into a box without top,by cutting a square from each corner and folding up the flaps to form the box.What should be the side of the square to be cut off so that the volume of the box is the maximum possible?

A square piece of tin of side 12 cm is to be made into a box without a lid by cutting a square from each corner and folding up the flaps to form the sides. What should be the side of the square to be cut off so that the volume of the box is maximum ? Also, find this maximum volume

A rectangular sheet of tin 58 cmxx44cm is to be made into an open box by cutting off equal squares from the corners and folding up the flaps.What should be the volume of box if the surface area of box is 2452 cm^(2) ?

An open box is to be made of square sheet of tin with side 20 cm, by cutting off small squares from each corner and foding the flaps. Find the side of small square, which is to be cut off, so that volume of box is maximum.

A box is to be made from a sheet 12times12 sq.cm, by cutting equals squares from the four corners and turning up its sides. Find the length of the side of the square to be cut out, in order to obtain a box of the largest possible volume?

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 1 (f) (Long Answer Type Questions (II))
  1. Show that a cylinder of a given volume which is open at the top has...

    Text Solution

    |

  2. The height of a closed cylinder of given volume and the minimum sur...

    Text Solution

    |

  3. Rectangles are inscribed inside a semicircle of radius r. Find the r...

    Text Solution

    |

  4. A square-based tank of capacity 250 cu m has to bedug out. The cost of...

    Text Solution

    |

  5. A tank with rectangular base and rectangular sides, open at the top...

    Text Solution

    |

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

    Text Solution

    |

  7. An open box is to be made of square sheet of tin with side 20 cm, by c...

    Text Solution

    |

  8. A canon is fired at an angle theta(0le theta le(pi)/(2)) with the hori...

    Text Solution

    |

  9. Find the maximum profit that a company can make, if the profit functi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Find the point on the curve y^2 = 4x which is nearest to the point (2;...

    Text Solution

    |

  13. Find the point on the curve y^2= 2x which is at a minimum distance fro...

    Text Solution

    |

  14. Find the point on the curve y^(2)=2x, which is nearest to the point (1...

    Text Solution

    |

  15. Find the point on the parabola x^(2)=8y, which is nearest to the point...

    Text Solution

    |

  16. A helicopter is flying along the curve y=x^(2)+2. A soldier is placed ...

    Text Solution

    |

  17. A manufacturer can sell 'x' items at a price of Rs (250-x) each. The c...

    Text Solution

    |

  18. A factory can shell 'x' items per week at price of Rs (20-(x)/(1000)) ...

    Text Solution

    |

  19. Let 'p' be the price per unit of a certain product, when there is a sa...

    Text Solution

    |

  20. If performance of the students 'y' depends on the number of hours 'x' ...

    Text Solution

    |