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Find the radius of a right circular cone if its volume is 1.5 times its lateral area and its radius is half its slant height.

  • Math -

    a = πrs = πr(2r) = 2πr^2
    v = π/3 r^2 h
    so,
    π/3 r^2 h = 3πr^2
    h=9

    If s = 2r,
    h^2 + r^2 = 4r^2
    9+r^2 = 4r^2
    r=3

    so, r=3 s=6 h=9

    check:
    a = π*3*6 = 18π
    v = π/3 * 9 * 9 = 27π

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