Cylinder

cylinder is a prism whose bases are curved surfaces rather than polygons.

circular cylinder has bases which are circles, and a right circular cylinder is a right angled prism whose bases are circles. A typical soda can is a right circular cylinder. The line joining the centers of the bases is called the axis of the cylinder. Generally, when we say cylinder, a right circular cylinder is implied.

Surface Area of a Cylinder

To find the area of the curved surface of a cylinder, consider cutting the curved surface along the vertical line and ‘unrolling’ the surface.

We will form a rectangle, where one side of the rectangle is the altitude, $\fn_phv h$ of the cylinder, and the other is the circumference, , of the bases. To visualize this better, wrap a piece of paper around it. This should make it clear that the curved surface of a cylinder is actually a rectangle. Thus, the Lateral Surface Area of a cylinder is $\fn_phv \mathbf{2 \pi rh}$ , and as the sum of the area of the curved surface and the two circular ends, we get

$\fn_phv \large \textbf{Total Surface Area}=\mathbf{2\pi rh+2\pi r^2}$

Volume of a Cylinder

Just as in the case of a cuboid, volume of a cylinder can be measured by filling it with circular sheets of paper.

$\fn_phv \large \textbf{Volume of a Cylinder}=\text{Base Area} \times \text{Height}$

$\fn_phv \large \\ =\text{Area of Circular base} \times \text{Height}\\ \\ = \boxed{\mathbf{\pi r^2 h}}$