Question 833495
{{{drawing(300,300,-1.5,8.5,-3,7,
circle(0,0,1),circle(2,0,1),
circle(4,0,1),circle(6,0,1),
circle(1,1.732,1),circle(3,1.732,1),
circle(5,1.732,1),
circle(4,3.464,1),circle(2,3.464,1),
circle(3,5.196,1),green(triangle(3,5.196,0,0,6,0)),
line(-1.5,-1,8.5,-1),red(arrow(2.4,-1.5,0,-1.5)),
red(arrow(3.6,-1.5,6,-1.5)),locate(2.5,-1.3,18cm),
red(arrow(6,0,6,-1)),red(arrow(6,-1,6,0)),locate(6.1,-0.3,3cm),
red(arrow(3,5.196,3,6.196)),red(arrow(3,6.196,3,5.196)),locate(3.1,5.9,3cm),
red(arrow(6.5,2.1,6.5,0)),red(arrow(6.5,3.1,6.5,5.196)),locate(6.2,2.9,9sqrt(3)cm)
)}}} The green triangle is an equilateral triangle.
Its sides measure {{{3*(6cm)=18cm}}} .
The height of an equilateral triangle is {{{side*sin(60^o)=side*(sqrt(3)/2)}}} .
The height of the green triangle is
{{{(18cm)*(sqrt(3)/2)=9sqrt(3)cm}}} .
THe radius of the pipes is {{{6cm/2=3cm}}} and the pile's height includes:
a radius of the pipes in the bottom row (below the green triangle), plus
a radius of the top pipe (above the green triangle).
So the total height is
{{{3cm+9sqrt(3)cm+3cm=highlight(6+9sqrt(3))}}}{{{cm}}}