3440.51 – Fraction of a Circular Area

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 $7 \pi 5^2 = 175 \pi$. The area of the large circle is $\pi 15^2 = 225 \pi$. The ratio is

$\frac{175\pi }{225\pi } = \frac{7}{9}.$

$Hmm$, 7 small circles; ratio $7/9$. Is something going on here?