SOLUTION: how high is a staggered, 20 layer stack of pipes if the diameter of each pipe is 12 cm?

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Question 1118283: how high is a staggered, 20 layer stack of pipes if the diameter of each pipe is 12 cm?
Answer by math_helper(2461) About Me  (Show Source):
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How high is a staggered, 20 layer stack of pipes if the diameter of each pipe is 12 cm?
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There is actually a formula for this:
The height, h(n), of n layers is +h%28n%29+=+r%2A%282+%2B+%28n-1%29sqrt%283%29+%29+
+h%2820%29+=++6%2A%282+%2B+%2819%29sqrt%283%29%29+=+6%2A%2834.909%29+, or approx +highlight%28+209.5cm+%29+


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The above formula can be derived from this:



Sanity check: Clearly (and coarsely) for a stack of pipes with 20 layers:
++10%2A%282r%29+%3C=+h+%3C=+20%2A%282r%29+
++20r+%3C=+h+%3C=+40r+
209.5cm = 34.9*r which falls in the above range.