Question

"Amachine produces open boxes using square sheets of metal. The machine cuts equal-sized squares measuring 2 inches on a side from the

comers and then shapes the metal into an open box by tuming up the sides. If each box must have a volume of 200 cubic inches, find the length
and width of the open box"

Answer 1

The length and width of the open box are both 10 inches.

Step-by-step explanation:

To find the dimensions of the open box, we need to start with the dimensions of the square sheet of metal.

The machine cuts equal-sized squares with a side length of 2 inches from the corners.

This means the length and width of the square sheet will be 2 inches longer than the length and width of the open box.

Let's denote the length and width of the open box as 'x'. Since the volume of the open box is 200 cubic inches, we have:

x * x * 2 = 200

Simplifying the equation, we get:

x² = 100

Taking the square root of both sides, we find:

x = 10

Therefore, the length and width of the open box are both 10 inches.