QuestionA spiral is made of semicircles with the first diameter $10 \mathrm{~cm}$, each next being $\frac{4}{5}$ of the last.
1) Find the total length of the spiral.
2) How far is point $E$ (midpoint of the 6th semicircle) from point $A$?

Studdy Solution
Calculate the distance from $A$ to $$.
$$AE = \frac{ - (\frac{4}{5})^6}{ - \frac{4}{5}} = \times \frac{ - (\frac{4}{5})^6}{\frac{}{5}} =50 \times ( - (\frac{4}{5})^6) \, cm$$So, the total length of the spiral is $25\pi \, cm$ and the distance from $A$ to $$ is $50 \times ( - (\frac{4}{5})^6) \, cm$.