If the height of two right circular cylinder are in the ratio of 1:2 and perimeters are in the ratio 3:4 . Find the ratio of their volumes.

Explanation

Let the heights of the two cylinders be h unit and 2h units [ ` :'` ratio ` = 1:2` ]
Also, let the radii of the cylinders be `r_(1)` units and `r_(2)` units.
As per questions, `2 pi r_(1) h : 2 pi r_(2) . 2h = 3:4`
or, `(2 pi r_(1))/(4 pi r_(2)) = 3/4 ` or, `(r_(1))/(r_(2))=3/2` ...........(1)
Now, ratio of volumes `= (pi r_(1)^(2)h)/(pi r_(2)^(2). 2h)=(r_(1)/r_(2))^(2)xx1/2= (3/2)^(2)xx1/2` [ by (1)] `= 9/4 xx 1/2 = 9/16 = 9:16`
Hence the required ratio `= 9:16`.