Mock AMC 8 #1 - Problem 16

Glenn has a very long rope, and cuts it into varying pieces. He positions the rope as shown below, where each separate piece is in a different color. Each time a new piece is added, it creates a semicircle with diameter 1 unit more than the last one. How many separate pieces are required such that the total length of the spiral is greater or equal to 60\pi?

(\textbf{A})\;15\quad(\textbf{B})\;16\quad(\textbf{C})\;17\quad(\textbf{D})\;18\quad(\textbf{E})\;19

Enter your answer as a capital letter.