A rectangular paper of `22cm xx 12cm` is folded in two different ways and formed two cylinders.
(i) Find the ratio of the volumes of two cylinders.
(ii) Find the difference of the volumes of two cylinders.

Options

A. `6:11`
B. `15:11`
C. `6:5`
D. `5:11`

Answer

A

Explanation

First way : When the paper is folded along 12 cm side, then height of cylinder `h_(1)=22cm`
and `2pi r_(1)=12`
`rArr r_(1)=(12)/(2pi)=(6)/(pi)cm`
`therefore` Volume `V_(1)=pi r_(1)^(2)h_(1)`
`= pi xx((6)/(pi))^(2)xx22=(792)/(pi)`
`=(792xx7)/(22)=252 cm^(2)`

Second way : When the paper is folded along 22cm side, then height of cylinder `k_(2)=12 cm`
and `2pi r_(2)=22`
`rArr 2xx(22)/(7)xxr_(2)=22`
`rArr r_(2)=(7)/(2)cm`
`therefore` Volume `V_(2)=pi r_(2)^(2)h_(2)`
`=(22)/(7)xx(7)/(2)xx(7)/(22)xx12`
`=462 cm^(3)`
(i) Ratio of volumes, `V_(1) : V_(2) = 252 : 462`
`= 6 : 11`
(ii) Difference in volumes `=(462-252)cm^(3)`
`=210 cm^(3)`