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Australian AMC 2019 - Senior Question 17

AMC AUSTRALIA · Australian AMC 2019 - Senior

Question 17

A circular steel gateway surrounding a rectangular gate is designed as shown. The total height of the gateway is divided into 10 equal intervals by equally-spaced horizontal bars.
The rectangular gate is what fraction of the area of the entire circular gateway?

Question illustration
  1. $\frac{48}{25\pi}$
  2. $\frac{\sqrt3}{\pi}$
  3. $\frac2\pi$
  4. $\frac{8\sqrt2}{25\pi}$
  5. $\frac8{5\pi}$