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Answer
Semi circumferences $P _1, P _2, P _3, \ldots$ are drawn by taking centres $A , B , A$, $B , \ldots$ It is given that radius of the first circle is $0.5 cm$. The radius of the second circle is $1.0 cm , \ldots$ From this information we will find $P _1, P _2, P _3, \ldots P _3$.
Length of the first semi circumference $=P_1=\pi r_1=\pi \times \frac{1}{2}=\frac{\pi}{2}$
$\begin{array}{l}
P_2=\pi r_2=\pi \times 1=\pi \\
P_3=\pi r_3=\pi \times 1.5=\frac{3}{2} \pi
\end{array}$
The lengths are $P_1, P_2, P_3, \ldots$, and the numbers $\frac{1}{2} \pi, 1 \pi, \frac{3}{2} \pi, \ldots$ are in A.P. Here $a=\frac{1}{2} \pi, d=\frac{1}{2} \pi$, From this let's find $S _{13}$.
$\begin{aligned}
S _{ n } & =\frac{n}{2}[2 a+(n-1) d] \\
S _{13} & =\frac{13}{2}\left[2 \times \frac{\pi}{2}+(13-1) \times \frac{1}{2} \pi\right] \\
& =\frac{13}{2}[\pi+6 \pi] \\
& =\frac{13}{2} \times 7 \pi= \\
& =\frac{13}{2} \times 7 \times \frac{22}{7} \\
& =143 cm .
\end{aligned}$
$\therefore$ The total length of spiral shape formed by 13 semicircles is $143 cm$.
Length of the first semi circumference $=P_1=\pi r_1=\pi \times \frac{1}{2}=\frac{\pi}{2}$
$\begin{array}{l}
P_2=\pi r_2=\pi \times 1=\pi \\
P_3=\pi r_3=\pi \times 1.5=\frac{3}{2} \pi
\end{array}$
The lengths are $P_1, P_2, P_3, \ldots$, and the numbers $\frac{1}{2} \pi, 1 \pi, \frac{3}{2} \pi, \ldots$ are in A.P. Here $a=\frac{1}{2} \pi, d=\frac{1}{2} \pi$, From this let's find $S _{13}$.
$\begin{aligned}
S _{ n } & =\frac{n}{2}[2 a+(n-1) d] \\
S _{13} & =\frac{13}{2}\left[2 \times \frac{\pi}{2}+(13-1) \times \frac{1}{2} \pi\right] \\
& =\frac{13}{2}[\pi+6 \pi] \\
& =\frac{13}{2} \times 7 \pi= \\
& =\frac{13}{2} \times 7 \times \frac{22}{7} \\
& =143 cm .
\end{aligned}$
$\therefore$ The total length of spiral shape formed by 13 semicircles is $143 cm$.
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