Home
Class 12
MATHS
A rectangular sheet of fixed perimeter w...

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are :

A

24

B

32

C

45

D

60

Text Solution

Verified by Experts

The correct Answer is:
A, C
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

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

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8: 15 is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are 24 (b) 32 (c) 45 (d) 60

A rectangular sheet of metal is 40cm by 15cm. Equal squares of side 4cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is

A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4 cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is

Four identical strips in the form of right isosceles triangles are removed from the four corners of a square sheet of side 8 cm. Find the area of the remaining sheet, if the length of each, equal sides of the triangles is 4 cm,

Find the maximum length of the side of a square sheet that can be cut off from a rectangular sheet of size 8mxx3m .

The area of a square park is the same as of a rectangular park.If the side of the square park is 60m and the length of the rectangular park is 90m, find the breadth of the rectangular park.

A box open from top is made from a rectangular sheet of dimension a xx b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :

MOTION-MAXIMA AND MINIMA -EXERCISE - 4 (LEVEL - II)
  1. The total number of local maxima and local minima of the function f(x)...

    Text Solution

    |

  2. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  3. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  4. Consider the function f : (-oo , oo) to (-oo , oo) defined by f(x) = (...

    Text Solution

    |

  5. Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and u...

    Text Solution

    |

  6. The maximum value of the function f(x)=2x^(3)-15x^(2)+36x-48 on the se...

    Text Solution

    |

  7. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  8. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  9. The number of distinct real roots of x^(4)-4x^(3)+12x^(2)+x-1=0

    Text Solution

    |

  10. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  11. Let I RvecI R be defined as f(x)=|x|++x^2-1|dot The total number of po...

    Text Solution

    |

  12. If f(x) = underset(0)overset(x)inte^(t^(2)) (t-2) (t-3) dt for all x ...

    Text Solution

    |

  13. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  14. The function f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a lo...

    Text Solution

    |

  15. Let f:RtoR and g:RtoR be respectively given by f(x)=|x|+1 and g(x)=x^(...

    Text Solution

    |

  16. A cylindrical container is to be made from certain solid material with...

    Text Solution

    |

  17. The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for al...

    Text Solution

    |