Australian AMC 2020 - Senior Question 12

Question 12

This diagram is composed entirely of semicircles. The diameter of each of the eight smallest semicircles is exactly one-quarter of the diameter of the two biggest semicircles.
What fraction of the large circle is shaded?

Question illustration

$\frac9{16}$
$\frac23$
$\frac34$
$\frac12$
$\frac58$