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Question
A rectangular strip 36cm x 22cm is rotated about the longer side. Find the volume and the total surface area of the cylinder formed.
Solution
Dimensions of rectangular strip = 36cm x 22cm
The rectangular strip is rotated about its length to form a cylinder, thus the length and breadth of the sheet will be equal to circumference and height (h) of the cylinder respectively.
Let r be the radius of the cylinder.
Circumference of cylinder = 36cm
2 x π x r = 36cm .......................................(1)
r = `(36)/(2π)`
r = `(18)/π"cm"`
thus,
Volume of the cylinder so formed
= π x r2 x h
= `πxx (18/π)^2 xx 22`
= 182 x 7
= 2268cm3
Now,
T.S.A. of cylinder
= (2 x π x r x h) + (2 x π x r x r)
= `(36 xx 22) + (36 xx 18/pi)` ...[from (1)]
= 792 + 206.18
= 998.18cm2.
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