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geometry

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Find the height of a cone with a volume of 138 cubic meters and a base area of 46 square meters

  • geometry -

    V = A * h

    h = V / A = 138 / 46 = 3 m

  • geometry -

    Volume of a cone:

    V = ( 1 / 3 ) * r ^ 2 * pi * h



    r ^ 2 * pi = B

    The area of the circle base



    V = ( 1 / 3 ) * B * h


    V = 138 m ^ 3

    B = 46 m ^ 2



    138 = ( 1 / 3 ) * 46 * h Multiply both sides by 3

    3 * 138 = 1 * 46 * h

    414 = 46 h Divide both sides by 46

    414 / 46 = h

    h = 414 / 46


    -------------------------
    Remark:

    414 = 2 * 3 * 3 * 23

    46 = 2 * 23

    -------------------------



    h = 2 * 3 * 3 * 23 / ( 2 * 23 )

    h = 3 * 3

    h = 9 m

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