Presentation on theme: " A Polyhedron- (polyhedra or polyhedrons) Is formed by 4 or more polygons (faces) that intersect only at the edges. Encloses a region in space. "— Presentation transcript:
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
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.
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.