# Q : 18       A spiral is made up of successive semicircles, with centres alternately at and ​​​​​​, starting with centre at , of radii   as shown in Fig. . 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   respectively.]

From the above given figure

Circumference of 1st semicircle

Similarly,

Circumference of 2nd semicircle

Circumference of 3rd semicircle

It is clear that this is an AP with

Now, sum of length of 13 such semicircles is given by

Therefore, sum of length of 13 such semicircles is 143 cm

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