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let first cylinder radius=r1
height=h1
volume=v1
second cylinder radius=r2
height=h2
volume=v2
given h1:h2=2:1
v1:v2=1:1
v1:v2=r1^2*h1:r2^2"h2
r1^2*h1/r2^2*h2=1
r1^2/r2^2=1/2
ratio of radii=1:√2
height=h1
volume=v1
second cylinder radius=r2
height=h2
volume=v2
given h1:h2=2:1
v1:v2=1:1
v1:v2=r1^2*h1:r2^2"h2
r1^2*h1/r2^2*h2=1
r1^2/r2^2=1/2
ratio of radii=1:√2
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