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.

2. 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

3. 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.

4. 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.

5. 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

6. 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

7. Surface Area of a Cylinder – S = 2B + Ch or S = 2r2 + 2r * h

8. 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.

9. 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

10. Surface Area of a Pyramid - S = B + ½ Pl Surface Area of a Cone - S = r2 + rl

11. 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.

12. 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

13. Composite space figure – is a three-dimensional figure of two or more simpler figures

14. 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.

15. 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

16. 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.

17. Chapter 11.6 Notes
Surface Area of a Sphere - S = 4r2 Volume of a Sphere - V = 4/3 r3 Hemisphere – cutting a sphere in half

18. 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.

19. Chapter 11.7 If the scale factor of two similar figures is 𝑎 𝑏 then,
the ratio of their perimeter is also 𝑎 𝑏
the ratio of their areas is 𝑎 2 𝑏 2
the ratio of their volume is 𝑎 3 𝑏 3