## Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting cong

Question

Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides. Then find the volume.

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2021-09-17T15:55:50+00:00
2021-09-17T15:55:50+00:00 1 Answer
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## Answers ( )

Answer:The dimension of the open rectangular box is.The volume of the box is 8.217 cubic inches.Step-by-step explanation:Given :The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.To find :The dimensions and the volume of the open rectangular box ?Solution :Let the height be ‘x’.

The length of the box is ’11-2x’.

The breadth of the box is ‘7-2x’.

The volume of the box isDerivate w.r.t x,

The critical point when V'(x)=0

Solve by quadratic formula,Derivate again w.r.t x,

Now,(+ve)(-ve)

So,there is maximum at x=1.392.The length of the box isThe breadth of the box isThe height of the box ish=1.392.The dimension of the open rectangular box is.The volume of the box is

The volume of the box is 8.217 cubic inches.