Math

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Benny wants to plant a garden around the base of a tree. To determine the amount of topsoi needed, he measured the circumference of the tree and found it to be 9.5 ft. His garden will be 2.0 feet wide in the form of a ring around the tree. Find to the nearest square ft. the surface area of the garden Benny intends to plant

  • Math -

    the circumference of the inner circle is 9.5 feet which is 2 pi Rtree where Rtree is the radius of the tree.
    From that find
    Rtree = 9.5 /(2*pi)
    then you can find the area of the tree cross section
    Atree = pi Rtree^2
    Then
    the outer radius of the path is
    Rout = Rtree + 2
    and the area of the big circle, which includes the tree cross section is:
    pi Rout^2
    the difference is the area of the garden
    pi(Rout^2 - Rtree^2)

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