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A box open from top is made from a recta...

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 :

A

`(a+b -sqrt(a^(2)+b^(2) -ab))/(12)`

B

`(a+b +sqrt(a^(2)+b^(2) -ab))/(6)`

C

`(a+b -sqrt(a^(2)+b^(2) +ab))/(6)`

D

`(a+b -sqrt(a^(2)+b^(2) -ab))/(6)`

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Knowledge Check

  • A box is constructed. from a rectangular metal sheet of 21 cm. by 16 cm. by cutting egual squares of sides x from the corners of the sheet and then turning up the projected portions . The value of xsathat volume of the box is maximum is

    A
    1
    B
    2
    C
    3
    D
    4

  • Read die following information carefully and answer the questions given below, A rectangular box is to be made from a sheet of 24 inch length and 9 inch width cutting out identical squares of side length x from ihe four corners and turning up the sides. What is the value of x for which the volume is maximum?

    A
    1 inch
    B
    1.5 inch
    C
    2 inch
    D
    2.5 inch

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