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Math Help - How many cubic yards?

  1. #1
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    Question How many cubic yards?

    Need help determining how many cubic yards of gravel I need for a flower bed in front of a building.

    The flower bed is 42' (feet) long, by 8' (feet) wide. The height closest to the building of gravel needs to be 16" (inches). The height of the gravel by the lawn needs to be 3" (inches). How many cubic YARDS of gravel to I need?

    Thank you.
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  2. #2
    A Plied Mathematician
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    From the building to the lawn: do you want a linear grade there, so that I could describe the shape of the gravel bed as a trapezoidal prism?
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  3. #3
    Senior Member eumyang's Avatar
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    The cross section of this prism of gravel would be a right trapezoid laid on its side. The two bases would be 3" and 16", and the "height" would be 8' = 96". The area would then be
    A = \frac{1}{2}(3 + 16)(96) = 912\,in^2

    The volume of the prism would be the area of this trapezoid times the width of the flower bed, which is 42' = 504":
    V = 912 \times 504 = 459,648\,in^3

    One cubic yard = 46,656 cubic inches, so
    V = (459,648\,in^3)\left( \dfrac{1\,yd^3}{46,656\,in^3} \right)\approx 9.852\,yd^3


    EDIT: Didn't see your post Ackbeet, sorry.
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  4. #4
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    thanks so much guys, sorry didn't get a chance to see ackbeet question before i saw eumyang's!
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