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A circular pond with a radius of 9 m is surrounded by a walking path that is 4.5 m wide. Determine the ratio of the area of the walking path to the area of the pond.

1. 4:3
2. 5:4
3. 7:4
4. 9:5

Correct answer: 5:4

Solution

The pond radius is 9 m and the path width is 4.5 m, so the outer radius is 13.5 m. Path area = \(\pi(13.5^2-9^2)=\pi(182.25-81)=101.25\pi\), while pond area = \(81\pi\). Their ratio is \(101.25:81 = 5:4\).

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