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.

Answer 1

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.