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# Two circular cylinders of equal volume … ## CBSE, JEE, NEET, CUET

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

Lakshaya Swarnareka 1 month, 2 weeks ago

Let r1 and h1 be the radius and height of the first cylinder, then Volume = πr21h1 Similarly r2 and h2 are the radius and height of the second cylinder ∴Volume=πr2h2 But their volumes are equal, ∴πr21h1=πr22h2 =r21r22=h2h1 ⇒h2h1=r22r21 But h1h2=12 ∴r22r21=12⇒r21=2r22 ∴r21r21=21⇒r1r2=√21 ∴ Ration in radii = √2 : 1 Hence the correct answer is √2 : 1

Aastha Vats 1 month, 2 weeks ago

Let the height be h and 2h and radii be r and R. 22/7 × r^2 × h = 22/7 × R^2 × 2h r^2 × h = R^2 × 2h r^2/R^2 = 2h / h r^2 / R^2 = 2/1 r/R = root 2 / 1 r:R = root 2 : 1

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