Q. 565.0( 2 Votes )

A. 1: √ 2

B. √ 2: 1

C. 1 : 2

D. 1 : 4

Answer :

Given: Two cylinders of equal volume.

Heights of the cylinders are in the ratio 1:2

Volume of cylinder is: πr^{2}h (here r and h are radius and height of the cylinder respectively)

Let V_{1} be the volume of first cylinder

∴ V_{1} = π(r_{1})^{2}h_{1}

Let V_{2} be the volume of second cylinder

∴ V_{2} = π(r_{2})^{2}h_{2}

Here,

V_{1}=V_{2}

⇒ π(r_{1})^{2}h_{1} = π(r_{2})^{2}h_{2}

⇒ (r_{1})^{2}h_{1} = (r_{2})^{2}h_{2}

⇒ (r_{1})^{2} : (r_{2})^{2} = h_{2} : h_{1}

⇒ (r_{1})^{2} : (r_{2})^{2} = 2 : 1

⇒ r_{1} : r_{2}= √2 :1

∴ ratio of the radii of given cylinders is √2 :1

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