# 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?

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 cm**

^{2}( Ans )
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