The ratio of the radii of two cylinders is 1:2,and the ratio of their height is 4:1. Ratio of their volumes
Answers
Answer:-
let h1 , h2 be the heights of two cylinders and r1 ,r2 be their radius.
_______________________________
given, ratio of heights h1 : h2 = 1 : 2
_______________________________
=> h1 / h2 = 1 / 2
and also given ratio of radii r1 : r2 = 2 : 1
_______________________________
=> r1 / r2 = 2 / 1
volume of first cylinder
(V1 ) = π r1^2 h1
volume of second cylinder
(V2 ) = π r2^2 h2
_______________________________
Find ratio of volumes :
_______________________________
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
_______________________________
Your Answer : V1 : V2 = 1 : 1
_______________________________