Acircular pond is to be surrounded by a gravel path. use the diagram to find the square feet of gravel needed if we know the pond has a radius of 200 ft and the radius of the whole space is 250 ft? a. 86,270 ft2 b. 57,234 ft2 c. 70,686 ft2 d. 65,523 ft2

C. 70,686 ft²

There are a couple of ways to get there.

Fairly straightforward is subtracting the pond area from the overall area of path and pond. The area of a circle is given by ...

... A = πr²

so that approach looks like ...

... A = π·250² -π·200² = 196,349.5 - 127,663.7 ≈ 70,685.8 ≈ 70,686 . . . ft²

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You can factor π from the above expression to make the arithmetic a little easier:

... A = π(250² -200²) = π(62500 -40000) = 22500π ≈ 70,686 . . . ft²

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You can further factor the difference of squares to give:

... A = π(250² -200²) = π(250 -200)(250 +200) = π·50·450 ≈ 70,686 . . . ft²

You might notice that this latter formulation is the product of the length of the centerline of the path and its width.

12*c

step-by-step explanation: