A rectangular sheet of paper 21 cm X 14 cm is rotated about its breadth, find the curved surface area and the total surface area of the cylinder so formed?

Answer :

We have : A rectangular sheet of paper 21 cm $\times$ 14 cm
And as given  : rectangular sheet of paper is rotated about its breadth , So from this information we know

Height of formed cylinder  =  Breadth  =  14 cm 
And
Radius of base  = 21 cm

We know curved surface area of cylinder  = $2 \mathrm{\pi } \mathrm{r} \mathrm{h}$
So,
Curved surface area of formed cylinder  = $2 \times \frac{22}{7}\times 21\times 14 = 2 \times 22 \times 3\times 14 = \mathbf{1848}\mathbf{ }\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{(}\mathbf{ }\mathbf{Ans}\mathbf{ }\mathbf{)}$
And
Total surface area of cylinder =  curved surface area  +  2 (  area of circular base )

So,

Total surface area of cylinder =  curved surface area  +  2 ( $\mathrm{\pi } {\mathrm{r}}^2$ )

Total surface area of cylinder =  1848 +  $2 \times \frac{22}{7}\times 21\times 21$

Total surface area of cylinder =  1848 +  $2 \times 22 \times 3 \times 21$

Total surface area of cylinder =  1848 + 2772

Total surface area of cylinder =  4620  cm²                                   ( Ans )