An open box is to be constructed from a square piece of shoo

An open box is to be constructed from a square piece of shoot metal by removing a square of side 3 feet from each comer and turning up the edges. (See the figure on the right.) If the box is to hold 243 cubic feet, what should be the dimensions of the sheet metal? What is the length of a side of the square piece of sheet metal?

Solution

Let x = the side length of the square of sheet metal.

The height will be 3, the length of the piece turned upward.
The length of the base will be x-2*3

VOLUME:.

3*(x-6)*(x-6)=243

3(x-6)^2=243

(x-6)^2=81

x-6=9

x=15

The uncut square sheet metal is 15 feet on each side.