Semicircular Design

Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?
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Semicircular Design


The diagram to the right shows a logo made from semi-circular arcs, each with a radius of $2$cm, $4$cm or $8$cm.

What fraction of the logo is shaded?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.