Amachine produces open boxes using square sheets of metal. the machine cuts equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. if each box must have a volume of 256 cubic inches, find the length and width of the open box.

The length and width of the open box is 8 inches.

Step-by-step explanation:

Given : A machine produces open boxes using square sheets of metal. The machine cuts equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides. If each box must have a volume of 256 cubic inches.

To find : The length and width of the open box?

Solution :

Let the length and the width of the box be x as it is square shaped.

The machine cuts equal-sized squares measuring 4 inches on a side from the corners and then shapes the metal into an open box by turning up the sides.

Now, the side of the box cut 4 inches from both side

Length = x-8,  Breadth = x-8 , Height = 4 inches

The volume of the box is 256 cubic inches.

The volume of the box is

Length of the box is x-8=16-8=8

Breadth of the box is x-8=16-8=8

Dimension of the box is

Therefore, The length and width of the open box is 8 inches.

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step-by-step explanation:

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