Problem: The diameter of a circle is divided into equal parts. On each part a semicircle is constructed. As becomes very large, the sum of the lengths of the arcs of the semi-circles approaches:
Answer Choices:
A. equal to the semi-circumference of the original circle
B. equal to the diameter of the original circle
C. greater than the diameter but less than the semi-circumference of the original circle
D. infinite in length
E. greater than the semi-circumference but finite
Solution:
For each semi-circle the diameter is , and the length of its arc is . The sum of such arcs is semi-circumference.