Question 18

A spiral is made up of successive semicircles, with centres alternately at $A$ and $B$, starting with centre at $A$, of radii $0.5 \text{ cm}$, $1.0 \text{ cm}$, $1.5 \text{ cm}$, $2.0 \text{ cm}$, $\ldots$ as shown in Fig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take $\pi = \dfrac{22}{7}$) [Hint: Length of successive semicircles is $l_1, l_2, l_3, l_4, \ldots$ with centres at $A, B, A, B, \ldots$, respectively.]