Determine the r-values?

Let V and S denote the volume and total surface area, respectively, of a right circular cylinder of radius r and height 1 unit. For which r-values will the ratio V/S be less than 1/3?

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  • Finlay
    Lv 5
    7 years ago
    Best Answer

    (πr^2h)/(2πrh+2πr^2)<1/3

    (πr^2)/(2πr+2πr^2)<1/3

    (πr^2)/2πr(1+r)<1/3

    r/2(1+r)<1/3

    r<1/3(2+2r)

    r<2/3+2r/3

    r-2r/3<2/3

    r(1-2/3)<2/3

    r<(2/3)/(1-2/3)

    r<6/3

    r<2

  • Anonymous
    7 years ago

    So V = pi*(r^2)*h = pi*r^2

    and S = 2*pi*r*h + 2*pi*r^2 = 2*pi*r + 2*pi*r^2 = 2*pi*r*(1+r)

    so V/S = pi*r^2 / 2*pi*r*(1+r) = r/(2(1+r))

    when is this less than 1/3?

    r/(2(1+r)) < 1/3

    3r/(2(1+r)) <1

    3r<2(1+r)

    3r<2+2r

    r<2

    and obviously r has to be positive so

    0<r<2

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