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# Write the formula to find the total surface area of a cylinder.

Last updated date: 20th Jun 2024
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Hint:A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom.
The general formula for the total surface area of a cylinder is
$2\pi rh + 2\pi {r^2}$
Where the radius of the cylinder is r and altitude (height) is $h$.

We need to derive the formula to find the total surface area of a cylinder.

Having radius $r$ and altitude (height) $h$, the surface area of a right circular cylinder, oriented so that its axis is vertical, consists of three parts:
The area of the top base: $\pi {r^2}$
The area of the bottom base: $\pi {r^2}$
The area of the side: $2\pi rh$
The area of the top and bottom bases is the same, and is called the base area, $B$. The area of the side is known as the lateral area, $L$.
An open cylinder does not include either top or bottom elements, and therefore has surface area (lateral area)
$L = 2\pi rh$
The surface area of the solid right circular cylinder is made up the sum of all three components: top, bottom and side. Its surface area is therefore,
$A = L + 2B = 2\pi rh + 2\pi {r^2}$
Thus The general formula for the total surface area of a cylinder is $2\pi rh + 2\pi {r^2}$ .

Note:A cylinder is one of the most basic curved geometric shapes, with the surface formed by the points at a fixed distance from a given line segment, known as the axis of the cylinder. The shape can be thought of as a circular prism. Both the surface and the solid shape created inside can be called a cylinder.