The quantity characteristic of the space limited to the surface of any body is called volume and is defined by a shape of this body and its linear sizes. In the international SI system for measurement of this size the square meter and derivatives of unit from it is recommended. Formulas of calculation of volume which can be applied to three-dimensional geometrical figures of the correct form are given below.
Instruction
1. If it is necessary to find the volume of a cylinder (V), then it is possible to make it, knowing the area of its basis (S) and height (h) - these sizes it is necessary to multiply: V=S∗h. As the area of the basis is defined by diameter (d) lying in the circle cylinder basis, volume can be determined as one quarter of the work of number of Pi on height and the squared diameter: V=π ∗ d² ∗ h/4.
2. For findings of volume cone (V) it is necessary to know height (h) and the area of its basis (S) too - it is necessary to calculate one third of the work of these sizes: V=S∗h/3. The same size can be expressed and through the radius of the circle (r) lying in the cone basis - it will make one third of the work of number of Pi on height and the squared radius: V=π ∗ r² ∗ h/3.
3. The volume of a pyramid (V) is one third of the work of height of a figure (h) on the area of its basis (S) too: V=S∗h/3. But as in the basis of this figure different polygons can lie, and the area of the basis should be calculated on different formulas, setting up them in the equality given above.
4. For calculation of volume of a sphere (V) it is enough to know its radius (r) - this size should be cubed, increased four times, to increase by Pi's number and to find a third of the received result: V=4 ∗π ∗ r³/3. Volume can be expressed and through diameter of a sphere (d) - it will be equal to the one sixth part from the work of number of Pi on the cubed diameter: V=π ∗ d³/6.
5. To calculate the volume of an ellipsoid (V) it is necessary to know three of its main axes (a, b and c) - a third of the work of their sizes it is necessary to increase by Pi's number and to increase four times: V=4∗a∗b∗c ∗π/3.
6. For scoping of a cube (V) it is enough to know length of one his edge (a) - it value should be cubed: V=a³.
7. The volume (V) physical body of any form can be determined if to know its mass (m) and average density of material (p) - these two sizes it is necessary to multiply: V=m∗p.