A large piece of cylindrical metal pipe is to be manufactured to include a strake, which...

A large piece of cylindrical metal pipe is to be manufactured to include a strake, which is a spiraling strip of metal that offers structural support for the pipe. (See Figure 3.51.) The pieces of the strake are to be made from flat pieces of flexible metal whose curved sides are arcs of circles as shown in Figure 3.52. Assume that the pipe has a radius of a ft and that the strake makes one complete revolution around the pipe every h ft.³

(a) In terms of a and h, what should the inner radius r be so that the strake will fit snugly against the pipe?

(b) Suppose a = 3 ft and h = 25 ft. What is r?