The circumferences of two circles are in the ratio 3:5. By what percentage is the area of the bigger circle greater than the area of the smaller circle?

200 %
185.56 %
156.75 %
177.78 %

Correct answer: 177.78 %

Solution

Since circumference is proportional to radius, the radii are in the ratio 3:5. Therefore, the areas are in the ratio $3^2:5^2 = 9:25$, so the bigger circle’s area exceeds the smaller by $\frac{25-9}{9}\times 100 = 177.78\%$.

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