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प्रश्न
Find the volume of the largest cylinder formed when a rectangular piece of paper 44 cm by 33 cm is rolled along its :
- shorter side.
- longer side.
उत्तर
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
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