# 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...

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

https://fbcdn-sphotos-b-a.akamaihd.net/hphotos-ak-ash4/374259_10200674054446015_1205438150_n.jpg

PLEASE, HELP ME!

### 1 Answer | Add Yours

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:**