Answer :


Length of rectangle sheet = 45 cm


Breath of rectangle sheet = 24 cm


Let the side length of each small square be a.


If by cutting a square from each corner and folding up the flaps we will get a cuboidal box with


Length, L = 45 – 2a


Breadth, B = 24 – 2a and


Height, H = a


Assuming,


Volume of box, V = LBH = (45 - 2a)(24 - 2a)(a)


Condition for maxima and minima is



(45 - 2a)(24 - 2a) + ( - 2)(24 - 2a)(a) + (45 - 2a)( - 2)(a) = 0


4a2 – 138a + 1080 + 4a2 – 48a + 4a2 – 90a = 0


12a2 – 276a + 1080= 0


a2 – 23a + 90= 0


a = 5, 18


= 24a - 276


For a = 5, = - 156,


For a = 18, = +156,


So for A to maximum



Hence, a = 5 will give maximum volume.


And maximum volume V = (45 - 2a)(24 - 2a)(a) = 2450 cm3


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