Chapter 11 1 Notes Common Core G GMD

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 = 2 B + 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 = 2 B + Ch or S = 2 r 2 + 2 r * 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 = r 2 + 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 = 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

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 r 2 h

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 = 4 r 2 Volume of a Sphere - V = 4/3 r 3 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.

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