Transcript Slide 1
Chapter 11.1 Notes Common Core – G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Objectives – To recognize polyhedra and their parts. To visualize cross sections of space figures. Chapter 11.1 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. Face – each polygon on the polyhedron 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 The intersection of a plane and a solid is called a cross section. Chapter 11.2 Notes Common Core – G.MG.1 Use geometric shapes, their measures, and their properties to describe objectives Objectives – To find the surface area of a prism and a cylinder. Chapter 11.2 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 = 2r2 + 2r * h Chapter 11.3 Notes Common Core – G.MG.1 Use geometric shapes, their measures, and their properties to describe objectives. Objectives – To find the surface area of a pyramid and a cone. Chapter 11.3 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 Pl Surface Area of a Cone - S = r2 + rl Chapter 11.4 Notes Common Core – G.GMD.1, G.GMD.3, G.GMD.2 & G.MG.1 Give an informal argument for the formulas for…volume of a cylinder…Use…Cavalieri’s principle… Use volume formulas for cylinders… Objectives – To find the volume of a prism and the volume of a cylinder. Chapter 11.4 Notes Volume of a Cube - V = B * h or V = s3 Volume of a Prism - V = B * h Volume of a Cylinder – V = B * h or V = r2h 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 Composite space figure – is a three-dimensional figure of two or more simpler figures Chapter 11.5 Notes Common Core – G.GMD.3 & G.MG.1 Use volume formulas for…pyramids, cones…to solve problems. Use geometric shapes, their measures, and their properties to describe objects. Objectives – To find the volume of a pyramid and of a cone. Chapter 11.5 Notes Volume of a Pyramid – V = 1/3 B*h Volume of a Cone - V = 1/3 B*h or V = 1/3 r2h Chapter 11.6 Notes Common Core – G.GMD.3 & G.MG.1 Use volume formulas for…spheres to solve problems. Use geometric shapes, their measures, and their properties to describe objects. Objectives – To find the surface area and volue of a sphere. Chapter 11.6 Notes Surface Area of a Sphere - S = 4r2 Volume of a Sphere - V = 4/3 r3 Hemisphere – cutting a sphere in half Chapter 11.7 Common Core – G.MG.1 & G.MG.2 Use geometric shapes their measures, and their properties to describe objects. Apply concepts of density based on area and volume in modeling situations. Objectives – To compare and find the areas nd volumes of similar solids. Chapter 11.7 𝑎 𝑏 If the scale factor of two similar figures is then, (1) the ratio of their perimeter is also (2) the ratio of their areas is 𝑎2 𝑏2 (3) the ratio of their volume is 𝑎3 𝑏3 𝑎 𝑏