Home
Class 12
MATHS
A square piece of tin of side 18 cm is t...

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

Text Solution

Verified by Experts

The correct Answer is:
`3cm,423"cm"^(3)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE (Multiple choice questions)|3 Videos
  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos
  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (SECTION VI)|9 Videos
  • APPLICATION OF INTEGRALS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTION FOR PRACTICE|36 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)|94 Videos

Similar Questions

Explore conceptually related problems

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

A square ·piece of tin of side 12 cm is to be made into a box without a top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of square to be cut off'. so that the volume of box is maximum and also find the volume of box.

A square sheet of tin of side 36 cm is to be made into a box without top by cutting off squares from each comer 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 sheet of tin of size 24 cm is to be made into a box without top by cutting off squares from each comer 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 sheet of tin whose side is 18 cm to be made into a box without top by cutting off squares from each comer 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 rectangular sheet of tin 45 cm x 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 the maximum possible.

BETTER CHOICE PUBLICATION-APPLICATIONS OF DERIVATIVES-ASSIGNMENT (SECTION VII) (Long Answer Type Questions)
  1. Find two positive numbers whose sum is 32 and product is large as poss...

    Text Solution

    |

  2. Find two numbers x and y such that x+y=15andx^(2)y^(3) is maximum.

    Text Solution

    |

  3. Find two positive numbers whose sum is 24 and their sum of squares is ...

    Text Solution

    |

  4. Find two positive numbers x and y such that x+y=36andxy^(3) is maximum...

    Text Solution

    |

  5. Find two positive numbers whose sum is 14 and sum of squares is minimu...

    Text Solution

    |

  6. Find the area of the largest rectangle having the perimeter 200 cm.

    Text Solution

    |

  7. Find the rate of change of the area of a circle with respect to its ra...

    Text Solution

    |

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

    Text Solution

    |

  9. A figure consists of a semi-circle with a rectangle on its diameter. G...

    Text Solution

    |

  10. A window consists if a semi-circle with a rectangel on its diameter. I...

    Text Solution

    |

  11. A square piece of tin of side 18 cm is to be made into a box without t...

    Text Solution

    |

  12. Show that the surface area of a closed cuboid with surface base and gi...

    Text Solution

    |

  13. Find two positive numbers whose sum is 14 and their sum of squares is ...

    Text Solution

    |

  14. Show that the height of the cylinder, open at the top of given surface...

    Text Solution

    |

  15. Find the rate of change of the area of the circle with respect to its ...

    Text Solution

    |

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

    Text Solution

    |

  17. Show that height of the cylinder of greatest volume which can be inscr...

    Text Solution

    |

  18. The radius of the circle is increasing at the rate of 0.7 cm/s . What ...

    Text Solution

    |

  19. A balloon which always remain spherical has a variable radius. Find th...

    Text Solution

    |