! [cylinder] (mons/thumb/9/91/cylinder _ geometry.svg/260px-cylinder _ geometry.svg.png)
The volume of a cylinder refers to the space occupied by this three-dimensional figure, usually expressed in cubic centimeters or cubic meters. Calculating the volume of a cylinder requires knowing the height and radius of the cylinder. The calculation method of cylinder volume is explained in detail below.
The formula for calculating the volume of a cylinder is as follows:
$V=\pi r^2 h$
Where $V$ represents the volume of the cylinder, $\pi$ is pi, $r$ is the radius of the bottom of the cylinder, and $h$ is the height of the cylinder.
Assuming that the radius of the bottom of the cylinder is $r$ and the height is $h$, we can divide the cylinder into thin slices, and the thickness of each slice is $dh$, as shown in the figure:
! [cylinder _ volume] (mons/thumb/5/5c/cylinder _ with _ height.svg/240px-cylinder _ with _ height.svg.png)
The volume of each slice can be approximately the volume of a disk, that is, $ dv = \ pir 2dh $,and the volume of the whole cylinder is divided by the sum of the volumes of many such disks, that is,
$ v = \ int _ 0 h dv = \ int _ 0 h \ pi r^2 DH = \ pi r 2 \ int _ 0 h DH = \ pi r 2h $
This is the volume formula of a cylinder.
For example, if the radius of the cylinder bottom is $4$ cm and the height is $ 10$ cm, its volume is:
$ v = \ pi r2h = \ pi \ times 4 2 \ times10 =160 \ pi $ cubic centimeter.
Since $\pi$ is infinitely close to $3. 14$, the volume of the cylinder is about $502.4$ cubic centimeter.
In addition to calculating the volume of cylinder by formula, other methods can be used to solve it quickly. For example, you can tilt the cylinder so that the bottom is just placed on a square piece of paper, then draw the outline of the cylinder with a pencil, and finally cut the square paper, and then unfold it to get a rectangle with the area of the bottom of the cylinder and the length equal to the height of the cylinder, so that the volume of the cylinder can be calculated by multiplying the bottom area by the height.
In a word, the volume of a cylinder is a basic geometric concept, which has important applications in daily life and scientific research. Mastering the volume calculation method of cylinder can not only help us better understand this geometric figure, but also help solve practical problems.