Vocabulary
Solids that are of the same type and have equal ratios of corresponding linear measures (heights, radii, etc.)
What are similar solids?
F + V = E + 2
The number of Faces + the number of Vertices of a solid = the number of Edges + 2.
What is Euler's Theorem?
2B + Ph.
What is the surface area of a right prism?
The volume of a prism.
What is Bh?
The intersection of a plane and a solid.
What is a cross section?
A solid in which each lateral edge is perpendicular to both bases.
What is a right prism?
The number of vertices in a polygon with 8 faces and 18 edges.
What is 12 vertices?
The surface area of a sphere.
What is 4πr2?
Bh, or πr2h.
What is the volume of a cylinder?
The net of a hexagonal prism.
What is six parallelograms joined together and two congruent hexagons, one sitting on top of the parallelograms and one sitting below?
Five types of solids.
What are a prism, pyramid, cylinder, cone, and sphere?
The Similar Solids Theorem (Theorem 12.13).
What is if two similar solids have a scale factor of a:b, then their corresponding areas have the ratio a2:b2, and their corresponding volumes have the ratio a3:b3?
The surface area of a right cone.
What is B + 1/2(Cℓ), or πr2 + πrℓ?
Volume of a pyramid.
What is 1/3(Bh)?
A circle that intersects a sphere and contains the center of the sphere.
What is a great circle?
Lateral faces.
What are parallelograms formed by connecting the corresponding base vertices of a polyhedron?
If two solids have the same height and cross-sectional area at every level, then they have the same volume.
What is Cavalieri's Principle?
B + 1/2(Pℓ).
What is the surface area of a regular pyramid?
1/3(Bh), or 1/3(πr2h).
What is the volume of a cone?
B = 1/2(aP).
What is the equation involving the apothem of a polygon commonly used to find the base area of a prism (and thereby the surface area and volume)?
The height of a lateral face of a regular pyramid.
What is slant height?
The ratio of the corresponding areas of two similar solids with a scale factor of a:b, according to the Similar Solids Theorem.
What is a2:b2?
The alternative form of 2B + Ch, the surface area of a right cylinder.
What is 2πr2 + 2πrh?
Volume of a sphere.
What is 4/3(πr3)?
The proportion involving arc length, circumference, sector area, and circle area of the same circle.
What is arc length/circumference = sector area/circle area?