Ans: 28%

The area of the larger circle is 25$ \pi $ cm $^2$.

The area of the smallest circle is 9$ \pi $ cm $^2$.

The area of the middle circle is 16$ \pi $ cm $ ^2 $.

Therefore the area of the ring is (16$ \pi $ - 9 $ \pi $) cm $ ^2 $ i.e. 7\ $ \pi $ cm $^2 $.

Therefore the percentage shaded is 28%.

*This problem is taken from the UKMT Mathematical Challenges.*

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