Volume or capacity is one of the characteristics of a substance or body in space.
The unit of measurement of the volume are cubic centimeters, cubic meters or liters, in the English system of units, the volume is also measured in gallons and barrels.
The method of measuring the volume depends on the shape of the object and its linear dimensions.
The volume occupied by a certain substance is measured in liters and is determined by its density and mass by the formula
V = mR, where m is the mass of the substance,? - its density.
The volume of geometric bodies is measured in cubic meters or cubic centimeters. The method of calculation depends on the shape of the body.
For simple geometric bodies, there are corresponding formulas, for example, the volume of a sphere of radius R is calculated by formula
V = (4/3) *? * R ?, where R is the radius,? Is the number?
The volume of a cone with a given radius of the base and height has the formula
V = (1/3) *? * R? * H, where R is the radius, h is the height of the cone,? Is the number?
The volume of an arbitrary body can be calculated using the integral calculus.
If the rotation body given by the function y = f (x) is given, then its volume can be determined by the formula given in the figure.
For a cylindrical body with a base R that is bounded from above by the surface z = f (x, y), the volume is calculated using a double integral.
The volume of some body U in Cartesian coordinates can also be calculated by means of a triple integral.