Chapter 6: Figures in Space
A cone is similar to a pyramid except that the base of the cone is a circle instead of a polygon. The lateral area (L) of a right cone is P rl. The total area (A) is P rl + P r2 = P r(l + r). The volume of a cone with base radius of length r and an altitude of length h is 1/3P r2h.
A sphere is the set of all points in space at a given distance from a given point called the center. The area of a sphere is 4P r2. The volume of a sphere with radius of length r is 4/3P r3.
Here are some additional properties about the polyhedrons:
An altitude of a prism or cylinder is any segment perpendicular to the planes containing the two bases with endpoints in these planes.
Two polyhedra are similar if all corresponding angles between faces and between edges are congruent, and the lengths of corresponding edges are proportional.
The radio of the lengths of corresponding edges of two similar polyhedra is a/b, then the ration of the lateral areas and total area is (a/b)2.
If a solid is the union of two or more nonoverlapping solids, then its volume is the sum of the volumes of these nonoverlapping parts.
Cavalieris Principle: If two solids have equal heights, and if the cross sections formed by every plane parallel to the basics of both solids have equal areas, then the volumes of the solids are equal.
Figures in space are interesting, and you will see them all the times in your lives. So why not master it? Please take a few minutes break and click here to continue to the next chapter. (You can also click on the drop-down list below to jump to any chapter you like.)
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