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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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- FinlayLv 59 years agoFavorite 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
- Anonymous9 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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