a solid that is bounded by polygons, called faces, that enclose a single region of space
an edge of a polyhedron is a line segment formed by the intersection of two faces
a vertex of a polyhedron is a point where three or more edges meet
if a polyhedron is regular if all of its faces are congruent regular polygons
a polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron
the of intersection of a plane and a solid
-tetrahedron (4 faces)
-octahedron (8 faces)
-dodecahedron (12 faces)
-icosahedron (20 faces)
F + V = E + 2
Volume Congruence Postulate
if two polyhedra are congruent, then they have the same volume
Volume Addition Postulate
the volume of a solid is the sum of the volumes of all its non-overlapping parts
if two solids have the same height and the same cross-sectional area at every level, then they have the same volume
volume of a prism or cylinder
volume of a pyramid or cone
the locus of points in space that are a given distance from a point (center of the sphere)
radius of a sphere
a segment from the center to a point on the sphere
chord of a sphere
a segment whose endpoints are on the sphere
two solids with equal ratios of corresponding linear measures, such as heights or radii
Similar Solids Theorem
if two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a^2:b^2, and corresponding volumes have a ratio of a^3:b^3
Please allow access to your computer’s microphone to use Voice Recording.
We can’t access your microphone!
Click the icon above to update your browser permissions and try again
Reload the page to try again!
Press Cmd-0 to reset your zoom
Press Ctrl-0 to reset your zoom
It looks like your browser might be zoomed in or out. Your browser needs to be zoomed to a normal size to record audio.
Your microphone is muted
For help fixing this issue, see this FAQ.