Question

A square piece of tin of side 18cm is to be made into
Ia box without ton cutting off square from each
worner and folding of the the flaps of the box
so that the volume of the box is mosimum
hossible.
What should be the side of the square to be cut off​

Answer 1

Answer:

Let the length of the each side of the square which is cut from each corner of the tin sheet be x cm. 

By folding up the flaps, a cuboidal box is formed whose length, breadth and height are 18−2x,18−2x and x respectively. 

Then, its volume V is given by

V=(18−2x)(18−2x)x

⇒dxdV=324−144x+12x2 and dx2d2V=−144+24x

The critical numbers of V are given by

dxdV=0

⇒324−144x+12x2=0

⇒x2−12x+27=0

⇒x=3,9

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