Volume of a cylinder
Kapitoly: Volume of a sphere, Volume of a cylinder, Volume of a cube, Volume of a cube, The volume of a prism
The volume of a cylinder tells us, popularly speaking, how many liters of water we can pour into the cylinder. So let's first look at what a cylinder looks like:
The formula for the volume of a cylinder
If you're just looking for a formula, then you can calculate the volume of a cylinder V, whose base has a radius r and which has a height v, as
$$\Large V=\pi\cdot r^2\cdot v$$
How did we figure this out?
It's actually simple. First we need to calculate the volume of the base - that's the circle, the wheel on which the cylinder rests. To do this, we use the formula for calculating the area of a circle, which is
$$S_\circ=\pi\cdot r^2,$$
where r is the radius of the base. In the figure, this is shown by the red horizontal line. Next, we can imagine that the cylinder itself is formed by stacking these circles on top of each other. If the height of the cylinder is to be equal to fifty, we stack fifty such circles on top of each other. The resulting volume of the cylinder is then obtained by multiplying the area of the base by the height of the cylinder, which is shown by the vertical red line in the figure:
$$V=S_\circ\cdot v=\pi\cdot r^2\cdot v$$
For example, if our cylinder had a height of v = 50 and the radius of the base was r = 10, then the volume of the cylinder would be equal to
$$V=\pi\cdot10^2\cdot50=5000\pi$$
If you don't like the result where pi is the constant, you can substitute an approximate value of 3.14 to calculate the approximate volume:
$$V\approx5000\cdot3{,}1415\approx15707$$