a rectangular piece of paper 22 cm long and 12 cm wide is rolled along the length to form a cylinder of height 12 cm find the volume of cylinder so formed also find the volume of cylinder formed when it is rolled along the breadth are the volumes the same
Please answer with proper steps
Answers
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Step-by-step explanation:
We have,
Length of rectangular paper = 22 cm.
Breadth of rectangular paper = 12 cm.
(i)
Given that it is rolled along the length to form a cylinder. Then the length of the piece forms the circumference of the base.
∴ 2πr = 22
⇒ 2 * (22/7) * r = 22
⇒ 2r = 7
⇒ r = (7/2) cm.
Now,
Given that height = 12 cm.
∴ Volume = πr²h
= (22/7) * (7/2)² * 12
= (22 * 7 * 12)/4
= 462 cm³
(ii)
Given that it is rolled along breadth. The the breadth becomes the height of cylinder.
∴ 2πr = 12
⇒ 2 * (22/7) * r = 12
⇒ 44 * r = 84
⇒ r = 84/44
⇒ r = 21/11
∴ Volume of cylinder = πr²h
= (22/7) * (21/11)² * 22
= 252 cm³
Therefore, their volumes are not same.
Hope it helps!