what will the dimension of the wood need to be?

Question

you want to build a box to hold your cd's. you want the measurements of the box to be 10in. long, 6in. wide, and 5in. tall. you do not want a lid for the box. using the measurements of the box, draw a diagram to determine the smallest sheet of wood that will be needed to make your box. what will the dimension of the wood need to be?

Answer 1

Let’s use a method similar to “exhaustive enumeration” (that is, list the dimensions of every one of the sides/bottom):

SideA:       10   x   5                                        50

EndB:        6    x   5                                         30

SideC:       10   x  5                                         50

EndD:         6  x  5                                           30

BottomE:     10  x  6     or    6   x  10              60

Top:          open

 TOTAL:                                                            220

 

Now, to check, we know that a box has 6 sides; we have listed them all.  We must find the dimensions of the smallest sheet of wood that will be needed to make this box.

 

First, let’s find the total area.  Why?   Because the dimensions that we find will also have that area.

 

10*5 + 6*5 + 10*5 + 6*5 + 10*6

   50   +  30  +  50   + 30    +  60

               220  sq in

 

The “board cutting problem” is a very common one.  How do you cut a board so that there is little or no scrap wood?  We must arrange the pieces that way so that we have the smallest board needed.

 

Looking at the numbers, we could use the distributive principle to group values (that is, place box sides next to each other).  We could use:

     5(10)  + 5(10)  + 6(5 + 5) + 6(10)

 

 This looks like:

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And is (5+5+6+6)=22 inches wide and (10 or 5+5)=10 inches tall with an area of 220 square inches, so there is 0 scrap.