Question

Solve the problem:
A machine produces open boxes using square sheets of plastic. The machine cuts equal-sized squares measuring 3 inches on a side from each corner of the sheet, and then shapes the plastic into an open box by turning up the sides. If each box must have a volume of 675 cubic inches, find the length of one side of the open box.

Answer 1

volume of the box is 675 cubic inches

A machine produces open boxes using square sheets of plastic.

It is a square sheet so length and width are same

Lets assume length as x so width is also x

The machine cuts equal-sized squares measuring 3 inches on a side from each corner of the sheet.

After turning up the sides the height of the box becomes 3 inches

We know the volume of a box formula

Volume = Length * width * height

We know length is  x , width is x  and height = 3

So V = x * x * 3

Given volume = 675 cubic inches

$675 = x * x * 3$

$675 = x^2* 3$

Divide by 3 on both sides

$225 = x^2$

Now we take square root on both sides

x = 15

the length of one side of the open box is 15 inches.