Question

The lateral areas of two similar cylinders are 196π in^2 and 324π in^2. The volume of smaller cylinder is 1715π in^3. Find the volume of the larger cylinder.

Answer 1

3,645 π in³

Explanation:

the ratio of the radius :

r1 : r2 = √196 : √324

= 14 : 18

= 7 : 9

the ratio of the volume:

v1 : v2 = 7³ : 9³

= 343 : 729

so, the volume of the larger cylinder =

729/343 x 1715π = 3,645 π in³

Answer 2

since the cylinders are similar their area and volume will be proportional

`(lateral\:area \:of \:smaller \:cylinder)/(laternal\: area \:of \:larger\: cylinder)=(volume \:of\: larger\: cylinder)/(volume \:of \:larger \:cylinder)`

`(196π)/(324π)=(1715π)/(V)`

V=1715π*324π/126π

V=4410πin³

the volume of the larger cylinder is 4410πin³.