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Arithmetic Progressions

Question 18:

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

Answer:

Semi-perimeter of circle = πr

I1 = π(0.5)

I2 = π(1) = π cm

I3 = π(1.5) =

Therefore, I1, I2, I3 ,i....

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