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.

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 is

Derivate 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 is

The breadth of the box is

The height of the box is h=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.

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step-by-step explanation: