SOLUTION: There are 4 identical wooden blocks that are 20 inches long, 2 inches wide and 1 inch thick. If you glue them together, what is the difference of the largest and smallest outer sur

Question 1177914: There are 4 identical wooden blocks that are 20 inches long, 2 inches wide and 1 inch thick. If you glue them together, what is the difference of the largest and smallest outer surface area you can get?
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.
There are 4 identical wooden blocks that are 20 inches long, 2 inches wide and 1 inch thick.
If you glue them together, what is the difference of the largest and smallest outer surface area you can get?
~~~~~~~~~~~~~~~~~

Obviously, to get the MAXIMUM surface area, you should glue the blocks together, attaching them at the minimal area faces.


So, you will get the MAXIMUM surface are, attaching the blocks at their 1x2 inches faces.


You will get then very long clued block with the length of 20*4 = 80 inches, the width of 2 inches and the thick of 1 inch.


Surface area of such a block is  2*(80*2 + 80*1 + 1*2) = 484 square inches.




To get the MINIMUM surface area, you should glue the blocks, attaching them together at their maximal area faces.


So, you will get the MINIMUM surface are, attaching the blocks at their 20x2 inches faces.


You will get then quite thick clued block with the length of 20 inches, the width of 2 inches and the thick of 4 inch.


Surface area of such a block is  2*(20*2 + 20*4 + 4*2) = 256 square inches.




Thus the difference of the largest and smallest outer surface area you can get is  484 - 256 = 228 square inches.

Nice entertainment problem.

RELATED QUESTIONS
There are 3 identical wooden blocks that are 50 inches long, 5 inches wide, and 2 inches... (answered by solver91311)

Ricardo wants to replace the wooden door on his flat. The wooden door will be shaped like (answered by drk,checkley77)

10. Margie wants to place a wooden door on her condo. The wooden door will be shaped like (answered by stanbon)

I am paralyzed & trying to order a Right Triangle of foam cut-to-order which will elevate (answered by ankor@dixie-net.com)

Ricardo wants to replace the wooden door on his flat. The wooden door will be shaped... (answered by checkley77)

1.the classroom is 20 feet long and 30 feet wide.the principal decided that the tiles... (answered by mananth)

Kyle has 2 loaves of cinnamon that he would like to cut into slices that are 1/3 inch... (answered by tommyt3rd)

What are the dimensions of a dining room that is 1.5 inch wide, 1.25 inches high, and 3... (answered by richard1234)

Margie wants to place a wooden door on her condo. The wooden door will be shaped like a... (answered by richwmiller)