3440.51 – Fraction of a Circular Area

Tags:Problem Set 9GeometryGeometry-Euclidean

What fraction of the large circle is covered by the small circles?


For convenience (we get to do this), let the diameter of the large circle be 30. Then the small circles have diameter 10, for example AC. The small circles total area is 7π52=175π7 π 5^2 = 175 π. The area of the large circle is π152=225ππ 15^2 = 225 π. The ratio is

175π225π=79.\frac{175π}{225π} = \frac{7}{9}.

HmmHmm, 7 small circles; ratio 7/97/9. Is something going on here?