Chapter 12.1 Notes Polyhedron – is a solid that is bounded by polygons, called faces, that enclose a single region of space. Edge – of a polygon is a line segment formed by the intersection of 2 faces Vertex – of a polyhedron is a pt where three or more edges meet.

A polygon is regular if all of its faces are ≌ regular polygons. A polygon is convex if there is no indentations. The intersection of a plane and a solid is called a cross section.

Platonic Solids – tetrahedron (4 faces), a cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), and a icosahedron (20 faces) Euler’s Thm – The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2

Chapter 12.2 Notes Surface Area of a Right Prism – S = 2B + Ph B – area of the base P – perimeter of the base h – height of the prism

Bases – the 2 polygons that are congruent Faces – are the polygons of the polyhedron Lateral Faces – are the polygons that are not the bases Surface Area – is the area of all the faces of the prism Right Prism – prisms where the lateral edges are ⊥ to both bases Oblique Prism - prisms where the lateral edges are not ⊥ to both bases

Surface Area of a Cylinder – S = 2B + Ch or S = 2  r  r * h

Chapter 12.3 Notes Pyramid – is a polyhedron in which the base is a polygon and the lateral faces are triangles. Regular Pyramid – has a regular polygon for a base and its height meets the base at its center

Surface Area of a Pyramid - S = B + ½ P l Surface Area of a Cone - S =  r 2 +  r l

Chapter 12.4 Notes Volume of a Cube - V = B * h or V = s 3 Volume of a Prism - V = B * h Volume of a Cylinder – V = B * h or V =  r 2 h Cavalier’s Principle – If 2 solids have the same height and the same cross-sectional area at every level, then they have the same volume

Chapter 12.5 Notes Volume of a Pyramid – V = 1/3 B*h Volume of a Cone - V = 1/3 B*h or V = 1/3  r 2 h

Chapter 12.6 Notes Surface Area of a Sphere - S = 4  r 2 Volume of a Sphere - V = 4/3  r 3 Hemisphere – cutting a sphere in half

Chapter 12.7 Notes Similar Solids Thm – If 2 solids have a scale factor of a:b, then corresponding areas have a ration of a 2 :b 2, and corresponding volumes have a ratio of a 3 :b 3. Scale Factor – a:b Areas - a 2 :b 2 Volume - a 3 :b 3