## Task 10 - V00910

A series of semicircles forms a spiral.

a) How large is the 10th semicircular arc if $r_{1}=1 \mathrm{~cm}, r_{2}=1.5$ cm, etc.?

b) How large is the total length of the spiral up to the 10th arc?

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0854.jpg?height=420&width=559&top_left_y=435&top_left_x=1254)
a) It is $r_{10}=1+9 \cdot 0.5=5.5$. The 10th radius is $5.5 \mathrm{~cm}$ in size.

b) $\left(r_{1}+r_{2}+\ldots+r_{10}\right) \cdot \pi \approx 102.1 \mathrm{~cm}$.