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 in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? Take π = 
[Hint : Length of successive semicircles is l1 , l2, l3, l4 ,…with centres at A, B, A, B, ….., respectively.]
Firstly, we have find circumference of each semi circle to find the total length
The circumference for semicircles is given by πr
where r is radius of each semi circle
the radii of circles is given by 0.5, 1.0,….6.5
l1 = πr1 = 
= 1.57cm
l1 = πr2 = 
= 3.14cm
Likewise we calculate all the other circumferences
1.57, 3.14,…… 20.41
The first term (a) = 1.57
Common difference (d) = a2 – a1 = 3.14 -1.57 = 1.57
The sum of 13 terms is given by (sn) = 
[2a + (n-1) d]
S13 = 
[2×1.57 + (13-1) 1.57]
= 6.5×21.98
= 142.87 = 143 (app.)
So, the total length of the spiral made is 143 cm