Home
Class 12
MATHS
A rectangular sheet of tin 45 cm by 24 c...

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top by cutting off squares from the corners and folding up the flaps. What should be the side of the square in order the volume of the box is maximum.

A

`x=18`

B

`x=24`

C

`x=5`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Let the side of square be `x`
Then the remaining dimensions of cuboid for volume is
Length = `45-2x`
width=`24-2x`
...
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT ENGLISH|Exercise EXERCISE 6.1|18 Videos

  • APPLICATION OF DERIVATIVES

    NCERT ENGLISH|Exercise EXERCISE 6.2|19 Videos

  • APPLICATION OF DERIVATIVES

    NCERT ENGLISH|Exercise EXERCISE 6.4|9 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

Similar Questions

Explore conceptually related problems

A square piece of tin of side 18 cm 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 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) ?

A square piece of tin of side 18 cm 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 box, constructed from a rectangular metal sheet, is 21 cm by 16cm by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. The value of x os that volume of the box is maximum is (a) 1 (b) 2 (c) 3 (d) 4

A square piece of cardbroad measuring x inches by x inches is to be used to form an open box by cutting off 2-inch squares, and then folding the slides up along the dotted lines, as shown in the figure above. If x is an integer , and the volume of the box must be greater than 128 cubic inches , what is the smallest value of x that can be used ?

A box of maximum volume with top open is to be made by cutting out four equal squares from four corners of a square tin sheet of side length a feet and then folding up the flaps. Find the side of the square cut-off.

From a rectangular sheet of tin, of size 100 cm by 80 cm, are cut four squares of side 10 cm from each corner. Find the area of the remaining sheet.

An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.

A rectangular cardboard sheet has length 32 cm and breadth 26 cm. The four squares each of side 3 cm are cut from the corners of the sheet and the sides are folded to make a rectanguler container. Find the capacity of the container.

A metallic sheet is of the rectangular shape with dimensions 48 c m\ x\ 36 c mdot From each one of its corners, a square of 8c m is cut off. An open box is made of the remaining sheet. Find the volume of the box.

NCERT ENGLISH-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum and minimum values of f(x)=x+sin2x in the interval...

    Text Solution

    |

  2. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

    Text Solution

    |

  3. Find the maximum value of 2x^3-24 x+107in the interval [1, 3]. Find t...

    Text Solution

    |

  4. Find the maximum and minimum values , if any , of the function f given...

    Text Solution

    |

  5. Find the maximum and minimum values, if any, of the following functio...

    Text Solution

    |

  6. Find the points of local maxima or local minima, if any, of the fol...

    Text Solution

    |

  7. Prove that the following functions do not have maxima or minima: (i)...

    Text Solution

    |

  8. Find the absolute maximum value and the absolute minimum value of f...

    Text Solution

    |

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

    Text Solution

    |

  10. Find the maximum value and the minimum value and the minimum value of ...

    Text Solution

    |

  11. At what points in the interval [0,2pi], does the function sin 2x attai...

    Text Solution

    |

  12. What is the maximum value of the function sinx + cosx?

    Text Solution

    |

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

    Text Solution

    |

  14. A wire of length 28 m is to be cut into two pieces. One of the pieces...

    Text Solution

    |

  15. Prove that the volume of the largest cone, that can be inscribed in...

    Text Solution

    |

  16. Show that the height of a closed right circular cylinder of given s...

    Text Solution

    |

  17. Of all the closed cylindrical cans (right circular), of a given volum...

    Text Solution

    |

  18. Show that semi-vertical angle of right circular cone of given total su...

    Text Solution

    |

  19. The point on the curve x^(2) = 2y which is nearest to the point (0, 5...

    Text Solution

    |

  20. Show that the right-circular cone of least curved surface and given...

    Text Solution

    |