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 $h$ in the picture)?

Solution

Referring to the figure below, $h = AB + BC + CD$ . 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, $h = 6 + 6\sqrt 3 + 6 = 12 + 6\sqrt 3$ .