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 Question from bailey, a student: hi there, A circular pond is surrounded by a path 1 metre wide. The area of the path is 1/4 of the area of the pond. Find the radius of the pond. Thanks

Hi Bailey,

The area of a circle is $\pi$ times the square of the radius. Suppose the radius of the pond is $r$ metres. Write an expression for the area of the pond.

The region containing the pond and the path is a circle of radius $r + 1$ metres and hence the area of the path is the area of a circle of radius $r + 1$ metres minus the area of a circle of radius $r$ metres. Write an expression for the area of the path.

Use the two expressions you have just found to write the equation "The area of the path is 1/4 of the area of the pond."

Solve for $r.$

Penny

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