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 Figure. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take `pi=22/7`)

Explanation

Circumference of the semicircle = `1/2xx2pir = pir`

Circumference of first semicircle = `pixx0.5`

Circumference of second semicircle = `pixx1.0`

Circumference of third semicircle = `pixx1.5`

And so on Circumference of `13th` semicircle = `pixx6.5`

Hence, series with common difference of `0.5pi`

Hence, sum of the series is

`S=n/2(a+l)`

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