What is the maximum number of video game cases that can fit into a shipping box? Show and/or explain your work.
Sunday, January 17, 2010
Problem 1: Volume
A game manufacturer places video game discs in cases with dimensions 15 cm × 8 cm × 2 cm. The video game cases are then packed into larger boxes for shipping. The dimensions of these shipping boxes are 30 cm × 25 cm × 9 cm. (click on the image to view the dimensions)
What is the maximum number of video game cases that can fit into a shipping box? Show and/or explain your work.
What is the maximum number of video game cases that can fit into a shipping box? Show and/or explain your work.
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28 is the maximum # of cd cases in 1 box. what i did is 15 cm × 8 cm × 2 cm divided by 30 cm × 25 cm × 9 cm. 15x8x2 is 240, then 30x25x9 is 6750. then didvide the 2 # and i get 28.125. and 28 is the whole # so that is the answer. (also cause you cant put like half a cd inside)
ReplyDelete#=number
~Adele~
You can fit 27 boxes.
ReplyDeleteFirst you find the volume of the big box, which is 30 cm times 25 cm times 9 cm = 6700 cm cubed.
Then the volume of the small box is 15 cm times 8 cm times 2 cm = 240 cm cubed.
So I had to find out how many 240 cm cubed could fite into 6700 cm cubed. I did 6700 divided by 240 and got 27 remainder 220.
Evy
24 cd cases can fit into one box. for the width, two cases can go side-by-side, and another two boxes can fit behind them. That equals a total of 6 boxes on one layer. For the height, it's 9cm and each box is 2cm. 2 can go into 9, 4 times with a remainder of one centimeter. summarizes this, there's 6 boxes per layer times four layers= 24 boxes total with some leftover room!
ReplyDelete~Iris
The Answer is you can fit 12 game boxes in a shipping box. First I found out the volume of the game box by multiplying Length(15cm)by Width(6cm) by Height (2cm). Then I found the volume of the shipping box. 25cm(width) by 9cm(height) by 30cm(Length). The volume of the game is 550cm3 the volume of the box is 6750cm3. Then I divided the 2 volumes by each other. The Answer was 12r150 so you can fit 12 game boxes into the shipping box.
ReplyDeletethe maximum amount of video games to fit in one shipping box is 27 video games.
ReplyDeletemy work, show here below.....
15x8=120cm2 x2=240cm3
30x25=750cm2 x9=6750cm3
6750cm3 / 240cm3 = 27cm3 (take of the cm3, and that's the # of video games per shipping box) with the remainder of 220 cm3.
First you have to find out how much space a video game case takes up. In other words, find the volume. Volume = length * height * times width. 15cm * 8cm * 2cm = 240 cubic centimeters.
ReplyDeleteThen you need to find the capacity of the larger boxes. Like volume the formula for capacity is length * height * width. So the capacity is 30cm * 25cm * 9cm. That equals 6750 cubic centimeters. Because capacity is measured in milliliters you convert the cubic centimeters into milliliters. 1 cubic centimeter = 1 milliliter making 6750 cubic centimeters, 6750 milliliters.
Then you divide 6750 by 240 = 28.125. Because you can not fit a part of a case the final answer is 2 8 cases can fit into the larger boxes.
* = times
15x8=120x2=240
ReplyDelete30x25=750x9=6750
240÷6750=28.30
they could fit about 28 video game cases in the shipping box.
Scarlett
Hey,
ReplyDeleteSo first I wanted to figure out the volume of the game cases. I multiplied 8 times 2 times 15 to get 240. So, the area of the case is 240 cm cubed. Then, I multiplied 25 times 30 times 9 to get 6750. The volume of the shipping boxes is 6750. Then, to find out how many cases will fit in a box I divided 6750 by 240 to get 28. So the maximum number of cases that can go in a box is 28.
*Katty*
The answer is 31. I know this because if you have 2 rows horizontally of 8 (16) CD cases. You still have room for 1 vertical row of 15. 15+16=31. That is how I found the answer.
ReplyDeleteMy answer is 24. Although there is 2 possible ones.This is my first This is because 2 goes into 9 only 4 times. And because the width is 15 cm which goes into 30 twice (2 times) that means that 8 boxes of the size 8x2x15 can go into the box of the dimentions 8x8x30. All you have to do now, since the height and width are at the max, is to see how many times 8 can go into 25(the lenght). That would be 3. So now you multiply 3x8. its 24. So my answer is 24 visually.
ReplyDeleteBut if you do it with capacity, the answer is 28 R:30cm3. this is because 30x25= 750 and 750x9=6750. So k=now i have fouind out the capacity of the big box (6750cm3). The dimentions of the small box are 8x2x15. Meaning that the volume is 240cm3 (because 15x2=30cm3 and 30x8=240cm3) and now you have to divide: 6750/240= 28 R:30. But i do not think this second way is correct since you can not make the case have 1cm in hight and 16cm in lenght so...
my final answer is 24.
oops sorry i think i said that the capacity of the small box is (Blank) but i meant to say volume. in other words i screwed up volume and capacity. if i said volume i meant capacity and if i said capacity i meant volume
ReplyDeleteOMG sorry i screwed up AGAIN!
ReplyDeletecapacity is how much something can hold and volume is how much space something takes up.
so i guess u know 8 goes into 25 3 times and 2 goes into 9 4 tiems and so the height wise u can fit 4 stacked ontop of eachother and then u can fit 3 length wise so and 15 goes into 30 twice so u can fit 2 rows of 4 cases high 3 times length cases which is..... 24.... viva pinata:)
ReplyDeletei say 28 can fit in there. because 15cm times 2cm times 8cm= 240cm2
ReplyDelete25cm times 9cm times 30cm= 6750cm2
6750cm2 divied by 240cm2= 28cm2
so i think its 28
Big box area: 9x30=180cm 180x25=4500cm2
ReplyDeleteSmall box area: 2x15=30 30x8=240
How many small boxes fit in the big box: 4500 divided by 240=18.75
18 boxes can fit in the big box
sorry I forgot instead of saying squared I meant to say cubed.
ReplyDeleteAt first, I tried stacking the video game cases lying flat and got 2 rows, 4 high, 3 deep which equals 24 boxes. Next I tried stacking the video game cases lying on the 15cm edge and got 2 rows by 12 deep which equals 24 as well. Then I got thinking. I did it the theoretical way by getting the volume of the big box (6750 cm cubed) and the video game case (240 cm cubed). Therefore the theoretical maxium number = 6750cm cubed divided by 240 cm cubed = 28.125 or 28 boxes. But that can't be true, because there must be some empty spaces that cannot be used. So next I figured out a combination of on edge and flat that gives you the maximum number. A solution I came up with is 15 boxes lying on edge across, 8 in 2 rows stacked flat and 2 in one row lying on edge at the back which totals to 25 boxes. I think this is the maximum number that you can pack into the shipping case.
ReplyDeleteVolume of big rectangular prism = 3375
ReplyDeleteVolume of small rectangular prism = 120
120 x 28 = 3360 so there will be 28 videogame cases that will fit, but there will be space left over.
This is devon using the classes computer so my identity might not show up. My awnser is 24. I found out that the width of the box is 30 so it can fit 2 of the video games width. Then i found out the hight was 9 so I found out that the it could fit 4 of the video games hight. I then used the boxes length of 25 meant that it could fit 3 of the video games length. So I did 2x3x4 and i got 24.
ReplyDeleteThe maximum number of cases that can fit is 28 because you cannot fit .125 of a case in and here is how i did it found out the area of small box(LxHxW=240) then found out the area of large box(6750) and divided 6750/(divided by)240 to get 28.
ReplyDeleteWell, I flipped the game cases around so they were 8 cm high, 2 cm across and 15 cm back. In the shipping box 15 game cases could fit across (30÷2=15), 1 game case high (9÷8=1.125) and 1 game case back (25÷15=1.666). That's only 15 game cases, and it leaves a 10 cm by 30 cm by 9 cm area of empty space which can be used. So I flipped the game cases again so they were 15 cm across, 2 cm back and 8 cm high again. So in that extra space, I could fit I game case high (9÷8=1.125), 2 game cases across (30÷15=2) and 5 game cases back (10÷2=5). That's another 10 cases. So the total number of these video game cases is 25 (15+10=25).
ReplyDeleteTheanswer to number one is that: 28 video game cases can fit into the big box.
ReplyDelete