Volume is a physical quantity that is inherent in a body with nonzero dimensions along each of the three directions of space (all real objects). In the article, as an example of the volume formula, the corresponding expression for the cylinder is considered.
Body volume
This physical quantity shows what part of the space this or that body occupies. For example, the volume of the Sun is much larger than this value for our planet. This means that the space belonging to the Sun, in which the substance of this star (plasma) is located, exceeds the terrestrial spatial region.
The volume varies in cubic units of length, in SI it is meters in a cube (m 3 ). In practice, the volume of liquid bodies is measured in liters. Small volumes can be expressed in cubic centimeters, milliliters and other units.
To calculate the volume, the formula will depend on the geometric features of the object in question. For example, for a cube, this is the triple product of the length of its edges. Below we consider the shape of a cylinder and answer the question of how to find its volume.
Cylinder concept
The figure that will be discussed is rather complicated. According to the geometric definition, it is a surface formed by parallel movement of a straight line (generatrix) along a certain curve (directrix). The generator is also called the generatrix, and the director is called the guide.
If the director is a circle, and the generator is perpendicular to it, then the resulting cylinder is called round and straight. It will be discussed further.
The cylinder has two bases that are parallel to each other and connected by a cylindrical surface. A straight line passing through the centers of two bases is called the axis of a round cylinder. All points of the figure are at the same distance from this line, which is equal to the radius of the base.
A round straight cylinder is uniquely determined by two parameters: the radius of the base (R) and the distance between the bases is the height H.
Cylinder volume formula
To calculate the area of space occupied by the cylinder, it is enough to know its height H and the radius of the base R. The desired equality in this case is:
V = pi * R 2 * H, here pi = 3,1416
To understand this volume formula is simple: since the height is perpendicular to the bases, if you multiply it by the area of one of them, you get the desired value V.
Barrel Volume Calculation
For example, we will solve this problem: we determine how much water will fit in a barrel with a bottom diameter of 50 cm and a height of 1 meter.
The barrel radius is R = D / 2 = 50/2 = 25 cm. Substitute the data in the formula, we get:
V = pi * R 2 * H = 3.1416 * 25 2 * 100 = 196350 cm 3
Since 1 l = 1 dm 3 = 1000 cm 3 , we obtain:
V = 196350/1000 = 196.35 liters.
That is, in a barrel you can pour almost 200 liters of water.