9.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05006f1f-ebf0-4d70-9dbb-68221c09043e-4_325_662_1345_520}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{figure}
Figure 3 shows part of a design being produced by a computer program.
The program draws a series of circles with each one touching the previous one and such that their centres lie on a horizontal straight line.
The radii of the circles form a geometric sequence with first term 1 mm and second term 1.5 mm . The width of the design is \(w\) as shown.
- Find the radius of the fourth circle to be drawn.
- Show that when eight circles have been drawn, \(w = 98.5 \mathrm {~mm}\) to 3 significant figures.
- Find the total area of the design in square centimetres when ten circles have been drawn.