Question

a rectangle sheet of paper 25 cm into 7 cm is rotated about the longer side find the volume of the cylinder thus generated

Answer 1

The solid so formed is a cylinder of height 25 cm and radius 7 cm and the formula of the total surface area is :

Answer 2

Rectangular sheet dimensions = 25 cm X 7 cm.

It is rotated about the edge 25cm. So it forms a 3-d solid. It is a solid cylinder of length (height) h = 25 cm and radius r = 7 cm. 

curved surface area CSA 
= 2 pi r h
= 2 × 22/7 × 7 × 25 cm^2
= 1, 100 cm^2.

Surface area of two flat sides
= 2 pi r^2
= 2 × 22/7 × 7^2 cm^2
= 308 cm^2

TSA total surface area
= 1,100+308 = 1,408 cm^2

we can also use formula 2 pi r (r+h).
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If we roll the given sheet into a hollow cylinder, then the surface area will be equal to:

  If rolling is done along the side of 7 cm:
        circumference of hollow cylinder = 7 cm
        radius of hollow cylinder = 7 /2π = 49/44 cm
         surface area = 2 π r h 
                              = 2 * 22/7 * 49/44 * 25 cm²

 If rolling is done along the side of 25 cm
         circumference = 25 cm
         radius = 25/2π cm  =175/44 cm
         surface area =  2 π r h = 2 * 22/7 * 175/44 * 7 cm²