GEOMETRY CHAPTER 11 SUMMARY

Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face. An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces.

A cube is a prism with six square faces. Other prisms and pyramids are named for the shape of their bases.

A net is a diagram of the surfaces of a three-dimensional figure that can be folded to form the three-dimensional figure. To identify a three-dimensional figure from a net, look at the number of faces and the shape of each face.

A cross section is the intersection of a three-dimensional figure and a plane.

The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. A right prism and an oblique prism with the same base and height have the same volume.

The volume of a pyramid is related to the volume of a prism with the same base and height. The relationship can be verified by dividing a cube into three congruent square pyramids, as shown. The square pyramids are congruent, so they have the same volume. The volume of each pyramid is one third the volume of the cube.

A sphere is the locus of points in space that are a fixed distance from a given point called the center of a sphere. A radius of a sphere connects the center of the sphere to any point on the sphere. A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres