A cylinder has a diameter of 20 cm. The area of curved surface is 100 sq cm. Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.
A cylinder has a diameter of 20 cm. The area of curved surface is 100 sq cm. Find: (i) the height of the cylinder correct to one decimal place. (ii) the volume of the cylinder correct to one decimal place.

The diameter of the cylinder = 20 cm

the radius (r) = 10 cm and the curved surface area = 100 cm2

Height = h cm

(i) Curved surface area

\[\begin{array}{*{35}{l}}

=\text{ }2\pi rh  \\

2\pi rh\text{ }=\text{ }100\text{ }c{{m}^{2}}  \\

2\text{ x }22/7\text{ x }10\text{ x }h\text{ }=\text{ }100  \\

h\text{ }=\text{ }\left( 100\text{ x }7 \right)/\text{ }\left( 22\text{ x }10\text{ x }2 \right)\text{ }=\text{ }35/22  \\

h\text{ }=\text{ }1.6\text{ }cm  \\

\end{array}\]

(ii) Volume of the cylinder

\[\begin{array}{*{35}{l}}

=\text{ }\pi {{r}^{2}}h  \\

=\text{ }22/7\text{ x }10\text{ x }10\text{ x }1.6  \\

=\text{ }502.9\text{ }c{{m}^{3}}  \\

\end{array}\]