#### Badatmath45

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If a 55 gallon water drum has a diameter of 23 1/4 inch and a height of 34 1/4 inch, how much space would it take to store 100 of them tightly packed together into a square?

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If a 55 gallon water drum has a diameter of 23 1/4 inch and a height of 34 1/4 inch, how much space would it take to store 100 of them tightly packed together into a square?

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Hello. If I understand the question correctly, all 100 drums are on the ground (so both their volume and their height are irrelevant), and you need to find the area (in square feet, maybe) of the enclosing square on the ground.

If so, then consider a simpler version, first. If you had only four drums and arranged them in two equal rows (i.e., two drums in front and two drums in back), how big would the enclosing square be? Draw the four touching circles, on a piece of paper. Do you see how the diameters of two circles next to each other relate to the side length of the enclosing square?

If you understand that, can you extend the idea to 100 circles?

PS: Be sure to check out the forum's submission guidelines (here's**a summary**). We'd like to see what you've tried or thought about, so far. Thanks!

If so, then consider a simpler version, first. If you had only four drums and arranged them in two equal rows (i.e., two drums in front and two drums in back), how big would the enclosing square be? Draw the four touching circles, on a piece of paper. Do you see how the diameters of two circles next to each other relate to the side length of the enclosing square?

If you understand that, can you extend the idea to 100 circles?

PS: Be sure to check out the forum's submission guidelines (here's

Last edited:

if so, this site may help you:

en.wikipedia.org

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I don't think it does. Look at the page Denis referenced (post #3). When the number of circles (n) is a square number, the arrangement is a √n × √n affair.… "hex" packing may not provide any advantage …

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You want me to listen to Denis??!!

I am complaining to Jomo.....

I am complaining to Jomo.....

Well, with no "packing" assumed, then each drum can be looked atIf a 55 gallon water drum has a diameter of 23 1/4 inch and a height of 34 1/4 inch,

how much space would it take to store 100 of them tightly packed together into a square?

as a 23.25 by 23.25 by 34.25 cuboid, meaning volume (space) of

18514.26525 cu. in. or 1851426.5250 cu. in. for 100

(or 1071.4275 cu. ft. or 39.6825 cu. yd.)

Game over!!

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Yes, I had wondered about the relationship between 'space' and 'square', in the op. So, I… each drum can be looked at as a 23.25 by 23.25 by 34.25 cuboid, meaning volume (space) … Game over!!

I'm waiting for the OP to respond.

Agree. Only ~3.12 in. as a "row reduction", but the reduction

may not provide any advantage (I have not checked it out though).

to 9 drums every 2nd row will more than offset that gain...