Q. 25.0( 1 Vote )
Two right circular cylinder of equal volume have their height in the ratio 1:2. What is the ratio of their radii?
Answer :
Let the two cylinders be with volume V1 and V2 with their respective radii and height as r1, r2 and h1, h2
Now given ratio of their heights i.e. h1:h2 = 1:2
∴ h1/h2 = 1/2
Volume of cylinder = πr2h
Given that volumes of both cylinder are equal i.e. V1 = V2
∴ π × r12 × h1 = π × r22 × h2
h1/h2 = r22/ r12
r22/ r12 = 1/2
r2/r1 = 1/√2
r1/r2 = √2/1
Therefore the ratio of their radii is r1:r2 = √2:1
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