How many cans can go in this box?

[mge3.14]

I have a question that says "There are 94 cans(each can has a diameter of 15 cm and a height of 30 cm). How many full boxes would you get when the box is 0.60 x 0.30 x 0.35 metres (L x W x H)? The answer is 11 full boxes and 6 cans loose.

My initial thought was if I get the volume of the box and the can, and then divide the volume of the box by the volume of the can, I'll get how many cans will go in one box. After that, I divide 94 by the number goes in per box. But this didn't work. Can anyone tell me why this doesn't work?

The box's volume I got was by 60*30*35 = 63000cm^3
The can't volume I got was by 7.5*7.5*3.14*30 = 5,298.75cm^3

 

[jonah2.0]

Beer soaked hint follows.

I have a question that says "There are 94 cans(each can has a diameter of 15 cm and a height of 30 cm). How many full boxes would you get when the box is 0.60 x 0.30 x 0.35 metres (L x W x H)? The answer is 11 full boxes and 6 cans loose.

My initial thought was if I get the volume of the box and the can, and then divide the volume of the box by the volume of the can, I'll get how many cans will go in one box. After that, I divide 94 by the number goes in per box. But this didn't work. Can anyone tell me why this doesn't work?

The box's volume I got was by 60*30*35 = 63000cm^3
The can't volume I got was by 7.5*7.5*3.14*30 = 5,298.75cm^3

You can only use the first 30 cm. height of each box to fit in 8 cans.

 

[Dr.Peterson]

I have a question that says "There are 94 cans(each can has a diameter of 15 cm and a height of 30 cm). How many full boxes would you get when the box is 0.60 x 0.30 x 0.35 metres (L x W x H)? The answer is 11 full boxes and 6 cans loose.

My initial thought was if I get the volume of the box and the can, and then divide the volume of the box by the volume of the can, I'll get how many cans will go in one box. After that, I divide 94 by the number goes in per box. But this didn't work. Can anyone tell me why this doesn't work?

The box's volume I got was by 60*30*35 = 63000cm^3
The can't volume I got was by 7.5*7.5*3.14*30 = 5,298.75cm^3

What you've done would work if you were pouring the contents of each can into the boxes. It doesn't take into account the space between cans (you can't fit a round can into a square hole) and above the cans.

Putting intact cans into a box requires you to think about how they can be arranged. Their answer assumes the most natural way to fit cans into the boxes. I would imagine what a full box looks like ...

 

[Steven G]

Just doing the division does not always work. Suppose you have a box whose size is 4ft x 3ft x 8ft = 96ft³
Now you have two boxes that are each 12ft x 2ft x 2ft = 48ft³. Now since 48*2 =96 you want to say that you can put these two boxes into the other box. But in fact you can't even put 1 box into the larger volume box! The division you are doing will tell you the most number of boxes that *may* fit. In my example there may be 2, 1 or 0 boxes that may fit (that is what at most 2 means in this case).