SOLUTION: A rectangular peice of sheet metal measures 26 in. by 20 in. A square measuring 2 in. by 2 in. is cut out of each corner, and the sides are folded to form a box. What is the volume

Question 139359: A rectangular peice of sheet metal measures 26 in. by 20 in. A square measuring 2 in. by 2 in. is cut out of each corner, and the sides are folded to form a box. What is the volume of the box? Please help because this is really difficult!!!!!!!!!!
Found 2 solutions by solver91311, checkley77:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

See diagram. The red squares are the cutouts, and the green lines are where you fold up the sides.

The volume of a rectangular solid is the length times the width times the height, or . Since you started with a 26 by 20 piece of material and cut 2 inch squares out of the corners, the length and width of the box become 26 - 4 = 22 and 20 - 4 = 16. The height of the box is just the 2 inches from the inside corner of the cut-out to the original edge of the material.

So just multiply 22 times 16 times 2. The unit will be cubic inches because your measurements are in inches. So, not that difficult after all, hmmm? Your teacher could have asked you to figure out what size squares to cut out of the corners so that you would have the maximum volume box. That is a much more interesting -- and difficult -- problem. If you are interested, write back and I'll show you how to do that one.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
THE BEST WAY TO MANAGE THESE TYPE OF PROBLEMS IS TO DRAW A SKETCH OF THE 26 BY 20 IN SHEET METAL AND THE 4 CORNERS CUT OUT.
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26 IN. BY 20 IN. PIECE OF SHEET METAL WITH 2 IN. CORNERS CUT OUT NOW HAS A LENGTH OF 26-4=22 IN. & 20-4=16 IN. FOR THE WIDTH & 2 IN. FOR THE HEIGHT.
THE VOLUME OF THIS BOX IS:
22*16*2=704 IN^3.

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