Question

What is the perimeter of a cylinder?

Answer 1

Finding the perimeter of a cylinder:

Cylinder: A cylinder is a three-dimensional geometric figure with parallel congruent bases connected with a curved surface.

Perimeter: Perimeter is the total boundary of any shape which is two-dimensional.

Now to find the perimeter of the cylinder, we have to make a cross-section vertically along the line parallel to the height of cylinder.

So a cylinder can be changed to a rectangle with length $\mathrm{l}=2\mathrm{\pi r}$, $\mathrm{r}$ is the radius of the top of cylinder and breadth $\mathrm{b}=\mathrm{h}$, $\mathrm{h}$ is height of cylinder.

Thus, perimeter of cylinder $=$Perimeter of rectangle

$\Rightarrow$ $=2\left(\mathrm{l}+\mathrm{b}\right)$

$\Rightarrow$ $=2\left(2\mathrm{\pi r}+\mathrm{h}\right)$

$\Rightarrow$ $=4\mathrm{\pi r}+2\mathrm{h}$

Hence, perimeter of cylinder is $4\mathrm{\pi r}+2\mathrm{h}$.