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A regular hexagonal pyramid whose base perimeter is 60cm has an altitude of 30cm. The volume of the pyramid is??

  • math -

    The volume of any "pointy thing" is
    (1/3) base x height

    our base is a hexagon where each side is 60/6 or 10 cm
    of course we have 6 equilateral triangles
    the area of one of these is
    (1/2)(10)(10)sin60° = 50√3/2 = 25√3
    and we have 6 of them, so the area of the base is
    150√3

    Volume = (1/3)(150√3)(30) = 1500√3 cm^3

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