A spiral is made up of successive semicircles, with centers alternately at A and B, starting with center at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, ... as shown in Fig. What is the total length of such a spiral made up of thirteen consecutive semicircles?

Circumference of first semicircle = πr = 0.5π
Circumference of second semicircle = πr = π
Circumference of third semicircle = πr = 1.5π
It is clear that a = 0.5π, d = 0.5π and n = 13
Hence, length of spiral can be calculated as follows:
S = n/2[2a + (n-1)d] = 13/2(2 × 0.5π + 12 × 0.5π) = 13/2 × 7π = 13/2 × 7 × 22/7 = 143 cm