The heights of two circular cylinders of equal volume are in the ratio 1 : 2. The ratio of their radii is

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sqrt(2) : 1 Let the radii of the two cylinders be r and R and their heights be h and 2h, respectively. Since the volumes of the cylinders are equal, therefore: `pi xx "r"^2xx"h" = pixx"R"^2xx2"h" => "r"^2/"R"^2 = $\frac{2}{1}$ => ("r"/"R")^2 = $\frac{2}{1}$ => "r"/"R" = sqrt(2)/1 => "r":"R" = sqrt(2:1)` Hence, the ratio of their radii is sqrt(2 : 1)

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