Question 1118283
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(n) = r*(2 + (n-1)sqrt(3) ) }}}   

 {{{ h(20) =  6*(2 + (19)sqrt(3)) = 6*(34.909) }}},  or approx {{{ highlight( 209.5cm ) }}} 
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The above formula can be derived from this:

{{{ drawing(400,400, -10,60, -10,60, grid(0), 
               circle(6,6,6),
               circle(18,6,6),
               circle(12,16.4,6),
               circle(6,26.8,6), 
               circle(18,26.8,6),         
              blue(line(5,32.8,34,32.8)),
              blue(line(18,26.8,34,26.8)),
              blue(line(18,6,34,6)),
            green(line(18,26.8, 18,16.4)),
            green(line(18,26.8, 18,6)),
            green(line(18,16.4, 12,16.4)),
            green(line(18,26.8, 12,16.4)), 
            green(line(12,16.4, 18, 6)), 

              locate(32,32,"r"),
              locate(20,20,"d = (n-1)*r*sqrt(3)"),
              locate(32,6,"r"),
              locate(10,50,"h = 2*r + d = 2*r + (n-1)*r*sqrt(3)")
           )
}}}

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Sanity check:  Clearly (and coarsely)  for a stack of pipes with 20 layers:
{{{  10*(2r) <= h <= 20*(2r) }}}
{{{  20r <= h <= 40r }}}

209.5cm = 34.9*r  which falls in the above range.