Question

A rectangular paper of 22 cm `xx` 12 cm 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.

Answer 1

Correct Answer - 525.53 `cm^(3)`
When the paper is folded along 12 cm side
Then height of cylinder `h_(1)`=22cm and `2pir1=12`
`r_(1)=(12)/(2pi)=(6)/(pi)cm`
volume `V_(21)=pir_(1)^(2)h_(1)=pixx((6)/(pi))^(2)xx22=(792)/(pi)=(792xx7)/(22)=252 cm^(3)`
When the paper is folded along 22 cm side
then height of cylinder `h_(2)`=12 cm and `2pir_(2)=22`
`2xx(22)/(7)xxr_(2)=22`
`r_(2)=(7)/(2)cm`
volume `V_(2)=pir_(2)^(2)h_(2)=(22)/(7)xx((7)/(2))^(2)xx12=(22)/(7)xx(7)/(2)xx(7)/(2)xx(7)/(2)xx12=462 cm^(3)`
(i) Ratio of volume `V_(1):V_(2)=252:462=6:11`
(ii) Difference in volumes =(462-252)`cm^(2) =210 cm^(3)`