A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of

Question

A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 250 cubic inches. How large should the piece of metal be? Round to the nearest hundredth.

 

___ inches by ___ inches

Answer 1

First, PLZ draw a picture (even if it is not to scale):

 

 

 

         xxxxxx

         xxxxxx

     xxxxxxxxxx

     xxxxxxxxxx

     xxxxxxxxxx

     xxxxxxxxxx

        xxxxxx

        xxxxxx

 

Then, list the important facts and formulas:

   The sheet of metal is square; with 2-inch squares cut out of the corners, the base will be square.

   The volume is:    length*width*height

       since length=width and height=2, this is:   V = side*side*2

 

   V = 250 = side*side*2

     side*side = 125

       side = 11.2 inches

 

The sheet of metal must be 2+11.2+2 inches by 2+11.2+2 inches.

The sheet of metal must be 15.2 inches by 15.2 inches.

 

Check:

  The box is 11.2*11.2*2 = 250.88 cubic feer.