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 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

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 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 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 :

The area of a rectangular sheet is 500m^(2). If the length of the sheet is 25cm, what is its width? Allar find the perimeter of the rectangular sheet.

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 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.

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.

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.

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. If 0\ <\ x\ <\ 1 , which of the following is greatest ? x (b) x^2...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Suppose the cubic x^3-px+q has three distinct real roots when p lt 0 a...

    Text Solution

    |

  5. Let f:""RvecR be defined by f(x)""={k-2x , if""xlt=-1 2x+3,f""x >-1} ....

    Text Solution

    |

  6. For x in (0,(5pi)/2) , define f(x)""=int0^xsqrt(t)sint"dt" Then f has ...

    Text Solution

    |

  7. Let a, b R be such that the function f given by f(x)""=""ln""|x|""+""...

    Text Solution

    |

  8. Find the equations of the tangent and normal to the curve x^(2/3)+y...

    Text Solution

    |

  9. Find the equation of tangent to the curve given by x=asin^3t ,""""y=bc...

    Text Solution

    |

  10. A curve in the plane is defined by the parametric equations x=e^(2t...

    Text Solution

    |

  11. Find the equation of the normal to curve x^2=4y which passes throug...

    Text Solution

    |

  12. Curve C1\ : y=e x\ ln\ x\ a n d\ C2: y=(lnx)/(e x)\ intersect at poin...

    Text Solution

    |

  13. A line is drawn touching the curve y-2/(3-x) . Find line if its ...

    Text Solution

    |

  14. Tangent at point on the curve y^2=x^3 meets the curve again at p...

    Text Solution

    |

  15. Determine the equation of straight line which is tangent at one point ...

    Text Solution

    |

  16. Find the equation of tangent and normal to the curve f(x)={x-2\ \ ...

    Text Solution

    |

  17. Find the point on the curve y=x^3-x^2-x+3, where the tangent is pa...

    Text Solution

    |

  18. Show that the line x/a+y/b=1 touches the curve y=b e^(-x/a) at the p...

    Text Solution

    |

  19. For the curve y=4x^3-2x^5, find all the points at which the tangent...

    Text Solution

    |

  20. The tangent at any point on the curve x=acos^3theta,y=asin^3theta meet...

    Text Solution

    |