Question

The ratio of the radii of two cylinders is 1:2,and the ratio of their height is 4:1. Ratio of their volumes

Answer 1

Answer:-

let h1 , h2 be the heights of two cylinders and r1 ,r2 be their radius.

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given, ratio of heights h1 : h2 = 1 : 2

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=> h1 / h2 = 1 / 2

and also given ratio of radii r1 : r2 = 2 : 1

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=> r1 / r2 = 2 / 1

volume of first cylinder

(V1 ) = π r1^2 h1

volume of second cylinder

(V2 ) = π r2^2 h2

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Find ratio of volumes :

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V1 : V2 = π r1^2 h1 : π r2^2 h 2

V1 : V2 = r1^2 h1 : r2^2 h2

V1 / V2 = ( r1^2 / r2^2 ) ( h1 / h2 )

V1 / V2 = ( r1 / r2 )^2 ( h1 / h2 )

V1 / V2 = (2 / 1 )^2 ( 1 / 2 )^2

V1 / V2 = 4 / 4 = 1 / 1

therefore ,

ratio of volumes V1 : V2 = 1 : 1

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Your Answer : V1 : V2 = 1 : 1

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