I don't know how to calculate the wasted space. Here are the problems. https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-prn2/969542_10200674056406064_228334538_n.jpg...

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First, we must calculate the volume of the box.  Let us assume that the cans fit into the box exactly, and so therefore the height of box is 2x10.5cm=21cm.

`V_b` =Length x width x height

We know that length = 22.5cm, width=14cm, and the height=21cm:

`V_b` =(22.5)(14)(21)=6615`cm^3`

Now we need to calculate the volume of 1 can:

`V_c=pir^2h`

We know that r=7.5/2=3.75cm and h=10.5cm:

`V_c=pi(3.75)^2(10.5)=463.9cm^3`

Finally, in order to calculate the amount of wasted space we must subtract the total volume of the 12 cans from the total volume of the box:

`V_w=V_b-12V_c=6615-12(463.9)=1048.2cm^3`

Therefore `1048cm^3` is wasted space.

In order to determine how much pacakging is required we must determine the surface area of the box:

`SA=2P_1+2P_2+2P_3`

Where `P_1` is the area of the panels on the left and right ends of the box, `P_2` is the area of the panels on the top and bottom of the box, and `P_3` is the area of the panels on the front and back of the box:

`P_1=(16.5)(21)=346.5cm^2`

`P_2=(14)(22.5)=315cm^2`

`P_3=(22.5)(21)=472.5cm^2`

Therefore, the amount of cardboard required is:

`SA=2(346.5)+2(315)+2(472.5)=2265cm^2`

Sources:

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