Question

Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its :

1. shorter side.
2. longer side.

Answer 1

i. Length of a rectangular paper = 44 cm

Breadth of a rectangular paper = 33 cm

When the paper is rolled along its shorter side, i.e. breadth, we have

Height of cylinder = h = 44 cm

Circumference of cross-section = 2πr = 33 cm

`=> 2 xx 22/7 xx r = 33`

`=> r = (33 xx 7)/(2 xx 22) = 5.25  cm`

∴ Volume of cylinder = πr²h

= `22/7 xx 5.25 xx 5.25 xx 44`

= 3811.5 cm³ 

ii. Length of a rectangular paper = 44 cm

Breadth of a rectangular paper = 33 cm

When the paper is rolled along its longer side , i.e. length, we have

Height of cylinder = h = 33 cm

Circumference of cross-section = 2πr = 44 cm

`=> 2 xx 22/7 xx r = 44`

`=> r = (44 xx 7)/(2 xx 22) = 7  cm`

∴ Volume of cylinder = πr²h

= `22/7 xx 7 xx 7 xx 33`

= 5082 cm³