 #  A Polyhedron- (polyhedra or polyhedrons)  Is formed by 4 or more polygons (faces) that intersect only at the edges.  Encloses a region in space. 

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 A Polyhedron- (polyhedra or polyhedrons)  Is formed by 4 or more polygons (faces) that intersect only at the edges.  Encloses a region in space.  Includes prisms and pyramids.  Does not include cylinders, cones, and spheres.

 V vertices  E edges  F faces  For any polyhedron, V - E + F = 2

 Regular polyhedron- all faces are congruent, regular polygons  Platonic solids are regular polyhedrons.  Tetrahedron (4 faces)- 3 triangles  Cube (6 faces)- 3 squares  Octahedron (8 faces)- 4 triangles  Dodecahedron (12 faces)- 3 pentagons  Icosahedron (20 faces)- 5 triangles

 Convex- any 2 points on the surface can be connected by a segment that lies entirely inside or on the polyhedron.  Cross section- intersection of a plane and a solid.

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Find the number of faces, vertices, and edges of the regular octahedron. Check your answer using Euler’s Theorem.

 Describe the shape formed by the intersection of the plane and the polygon.

 Lateral faces, edges, bases, lateral area and surface area  Right prism- lateral edges are perpendicular to both bases  Oblique prism- lateral edges are not perpendicular to the bases  SA = 2B + Ph

 height, base areas, lateral area, surface area  Right cylinder- the side of the cylinder is perpendicular to the bases.  Oblique cylinder- the side of the cylinder is not perpendicular to the bases  SA = 2B + Ch or SA = 2∏r 2 + 2∏rh

 Regular Pyramid- a regular polygon for the base and the segment from the common vertex to the base is perpendicular  Lateral faces- congruent isosceles triangles  Slant height, l- the altitude of the lateral face (triangle)  LA = Pl/2  SA = Pl/2 + B

 Cone- formed by a circular base and a curved surface that connects the base to a vertex  The radius of the base is the radius of the cone.  The height of the cone, h, is the perpendicular distance from the vertex to the base.  The slant height is the distance from the vertex to a point on the circle of the base.  LA = Cl/2  SA = Cl/2 + B or = ∏r 2 + ∏rl

A regular square pyramid has a height of 15 centimeters and a base edge length of 16 centimeters. Find the area of each lateral face of the pyramid

Find the surface area of the regular hexagonal pyramid.

Find the surface area of the right cone shown.

 Find the surface area of the cone.

 The volume of a cube is the cube of the length of its sides. V = s 3  If 2 polyhedra are congruent, then they have the same volume.  The volume of a solid is the sum of the volumes of all its non-overlapping parts.

 If 2 solids have the same height and the same cross-sectional area at every level, then they have the same volume.

 V = Bh  Find the volume of a right hexagonal prism with a height of 7cm and side length (of the hexagon) equal to 12cm.

 V = Bh = ∏r 2 h  Fi nd the volume of a right cylinder with a height of 10ft and a radius of 40ft.

 Find the volume of the oblique cylinder.

 Pyramids: V = (1/3) Bh  Cones: V = (1/3)Bh or (1/3) ∏r 2 h

 Find the volume of the hexagonal pyramid.

 Two cones sharing a common base have a radius of 10mm. One of the cones is 16mm high and the other is 18mm. Find the volume.

 Definitions- center, radius, chord, diameter,  Great circle- the intersection formed by a plane that intersects the sphere through its center  Hemisphere- two halves of the sphere

 SA = 4πr 2  Find the surface area of the sphere.

 V = 4πr 3 /3  Find the volume of a beach ball with a diameter of 15in.

 Find the surface area of a globe that has a circumference of 18π inches.

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