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A spiral is made up of successive semicircles, with centres alternatively 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 the figure. What is the total length of such a spiral made of thirteen consecutive semicircles? (Take ).
[Hint: Length of the consecutive semicircles is with centres at A, B respectively]
Asked by Yoga Last Modified
Answer 
Length of semicircle=circumference/2 = 2Πr/2=Πr
There are 13 semicircles with radius
0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,6,6.5
I.e. in AP whose 1St term=0.5 &
common difference=0.5
Now, total length of spiral=Π(0.5+1+1.5+2+2.5+3+3.5+4+4.5+5+5.5+6+6.5)
As we know sum of an AP is=
no. of terms(1St term+last term)/2= 13(0.5+6.5)/2=13×7/2=91/2
Now put value
Total length of spiral =(22/7)×(91/2)=11×13=143cm i.e. ans
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