The cone can be defined as a set of the points forming a two-dimensional figure (for example, a circle), integrated with a set of points which lie on the pieces which are beginning on perimeter of this figure, and coming to an end in one general point. This definition is right if the only general point of pieces (cone top) does not lie in one plane with a two-dimensional figure (basis). The piece perpendicular to the basis connecting top and the basis of a cone is called its height.
Instruction
1. You proceed at calculation of volume of different types of cones from the general rule: required size has to be equal to one third of the work of the area of the basis of this figure on its height. For a "classical" cone which basis is the circle its area is calculated by multiplication of number of Pi by the squared radius. From this follows that the formula for calculation of volume (V) has to include the work of number of Pi (π) on a square of radius (r) and height (h) which should be reduced three times: V = ⅓*π*r²*h.
2. Calculation of volume of a cone with the basis of an elliptic form requires knowledge of both of its radiuses (an and b) as the area of this roundish figure is multiplication of their work by Pi's number. Replace with this expression the area of the basis in a formula from the previous step, and you receive such equality: V = ⅓*π*a*b*h.
3. If in the basis of a cone the polygon lies, then such special case is called a pyramid. However the principle of calculation of volume of a figure from it does not change - begin and in this case with definition of a formula of finding of the area of a polygon. For example, for a rectangle the multiplication of lengths of two of its adjacent parties suffices (an and b), and for a triangle this size it is necessary to increase also by a sine of the angle between them. Replace a formula of the area of the basis in equality from the first step and receive a formula of calculation of volume of a figure.
4. Find the areas of both bases if it is necessary to find out the volume of the truncated cone. Smaller of them (S ₁) can call section. Calculate his work on the area of the bigger basis (S ₀), add to the received size both areas (S ₀ and S ₁) and take a square root from result. The received value can be used in a formula from the first step instead of the area of the basis: V = ⅓ * √ (S *S +S +S ₁)*h.