A spiral is made up of successive semicircles, with centres alternately at A and B,starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown inFig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take 
[Hint : Length of successive semicircles is 
with centres at A, B, A, B, . . .,respectively.]
Circumference of 1st semicircle = πr = 0.5π
Circumference of 2nd semicircle = πr = 1π = π
Circumference of 3rd semicircle =πr = 1.5π
It is clear that a = 0.5 π, d = 0.5π and n = 13
Hence; length of spiral can be calculated as follows:
= 
(7
)
= 
= 143 cm
36