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PreAlgebra

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A circular pond 20 m in diameter is surrounded by a gravel path 5 m wide. The path is to be replaced by a brick walk costing $30 per square meter. How much will the walk cost?

i need to teach this to my brother, but i'm stuck on it myself. please show me how this would be solved
i tried figuring out the area of the whole circle(including the pond and walk) and then subtracting the inner circle (pond)
but i don't get the correct answer


please help

  • PreAlgebra -

    Your method should work.

    area = 2 * pi * radius^2
    area ~ 6.28 * radius^2

    POND:
    diameter = 20m
    radius = diameter / 2
    radius = 20m / 2 = 10m
    area = 6.28 * (10m)^2 = 6.28 * 100m^2
    area = 628m^2

    POND and WALK:
    remember, the walk goes all the way around the pond, so there is 5m of wall on the west boundary and another 5m of wall on the east boundary. The diameter is increased by 10m, not just 5.
    diameter = 20m + 10m = 30m
    radius = diameter / 2
    radius = 30m / 2 = 15m
    area = 6.28 * (15m)^2 = 6.28 * 225m^2
    area = 1,413m^2

    WALK:
    The area of the walk is equal to the area of the pond AND walk minues the area of the pond alone.
    area = 1,413m^2 - 628m^2
    area = 785m^2

  • PreAlgebra -

    No I don't have an answer so I came to this very unhelpful website. Bye!

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