One of features of stereometry is an opportunity to approach the solution of tasks from different sides. Having analyzed the known data, you will be able to choose the most convenient method of calculation of volume of the truncated pyramid.
Instruction
1. The concept truncated piramidypiramidy is called a polyhedron which basis the polygon with any number of the parties, and side sides – triangles with the general top forms. The truncated pyramid represents a pyramid fragment between its basis and section parallel to it, side sides in it have the form of trapezes.
2. Way pervyyvospolzuytes formula: V = 1/3h ∙ (S1 + S2 + √S1 + S2), where h – height of the truncated pyramid, S1 – the area of the basis, and S2 – the area of the top side (the section forming this figure). Calculation is based on the theorem saying that the volume of the truncated pyramid is equal one third works of height for the sum of the areas of the bases and an arithmetic average between them. The proof can be made both for a trihedral pyramid (tetrahedron), and for a polyhedron with any other basis.
3. The way of a vtoroyinogd for the solution of a task on the volume of the truncated pyramid is more convenient to complete it to full, and then to calculate required as the difference of volumes of two polyhedrons. Having used the general formula of calculation of volume of a pyramid of V = 1/3 h ∙ S where S is the area of the basis of a pyramid, calculate at first the volume of a full pyramid, and then – its cut part.
4. A way you tretiyvychislit the volume of the truncated pyramid, having used a concept of similarity of figures. The full and formed above a secant planes (cut) of a pyramid are similar, as well as the bases of the truncated pyramid represent similar polygons. The general rule for similar volume figures sounds so: the relation of volumes of similar polyhedrons equals to the similarity coefficient built in the third degree. That is if the similarity coefficient is known, it is possible to use a formula: V1/V2 = k3. Operating with the data, known under the terms of a task, substitute the general formula of volume of a pyramid of V = 1/3 h ∙ to S.