3500.41 – Water Pipes Stack

Three new water pipes for Main Street are stacked as shown. The external diameter of each pipe is 12 inches. How tall is the stack hh in the picture)?

3500_41_f01bbbeae9.png

Solution

Referring to the figure below, hh = AB + BC + CD. Now, AB = 6 and CD = 6. Those two are easy.

Continuing, BC is the altitude of equilateral \triangle BXY with sides of length 12,

XC = 6, \triangle BXC is a 30 - 60 - 90 right \triangle , and

so BC = 6\sqrt 3.

Therefore, hh = 6 + 6\sqrt 3 + 6 = 12 + 6\sqrt 3.

3500_41_solution_e02d6b9ff2.png