Surface Area & Volume

1. Surface Area & Volume Chapter 12

2. Solid Figures Section 12-1

3. Solid Figures Also called solids Enclose part of space

4. Polyhedrons Solids with flat surfaces that are polygons

5. Parts of a Polyhedron Faces – 2-dimensional surfaces formed by polygons Edge – where 2 faces intersect Vertex – the point where 3 or more edges intersect

6. Prisms Two parallel faces called bases that are congruent polygons Other faces are called lateral faces Lateral faces intersect in lateral edges

7. Pyramids All faces except the base intersect at the vertex The triangular faces that meet at the vertex are called lateral faces

8. Cylinders The two bases are congruent, parallel circles The lateral surface is curved

9. Cone The base is a circle The lateral surface is curved The point is called the vertex

10. Surface Area of Prisms and Cylinders Section 12-2

11. Area Lateral Area - The sum of the areas of its lateral faces Surface Area – The sum of the areas of all its surfaces

12. Theorem 12-1 Lateral Area of a Prism L = Ph P= perimeter of the base h= height of the prism

13. Theorem 12-2 Surface Area of a Prism S = Ph + 2b B = area of the base

14. Theorem 12-3 Lateral Area of a Cylinder L = 2 rh r = radius of the base h= height of the cylinder

15. Theorem 12-4 Surface Area of a Cylinder S = 2 rh + 2 r2

16. Volume of Prisms and Cylinders Section 12-3

17. Volume The measurement of the space contained within a solid figure

18. Theorem 12-5 Volume of a Prism V = Bh B = area of the base h = height of the prism

19. Theorem 12-6 Volume of a Cylinder V =  r2h r = radius of the base h = height of the cylinder

20. Surface Area of Pyramids and Cones Section 12-4

21. Altitude The segment from the vertex perpendicular to the base In a right pyramid or cone, the altitude is perpendicular to the center In an oblique pyramid or cone, the altitude is perpendicular at another point

22. Regular Pyramid A right pyramid whose base is a regular polygon

23. Slant Height The height of each lateral face of a pyramid Represented by l

24. Theorem 12-7 Lateral Area of a Regular Pyramid L = ½ Pl P = perimeter of the base l = slant height

25. Theorem 12-8 Surface Area of a Regular Pyramid S = ½ Pl + B B = area of the base

26. Theorem 12-9 Lateral Area of a Cone L = rl r = radius of the base l = slant height of the cone

27. Theorem12-10 Surface Area of a Cone S = rl + r2

28. Volumes of Pyramids and Cones Section 12-5

29. Theorem 12-11 Volume of a Pyramid V = 1/3Bh B = area of the base h = height of the pyramid

30. Theorem 12-12 Volume of a Cone V = 1/3 r2h r = radius of the base h = height of the cone

31. Spheres Section 12-6

32. Sphere A sphere is a set of all points that are a given distance from a given point called the center.

33. Tangent A line that intersects the sphere at exactly one point

34. Theorem 12-13 Surface Area of a Sphere S = 4r2 r = radius of the sphere

35. Theorem 12-14 Volume of a Sphere V = 4/3 r3

36. Similarity of Solid Figures Section 12-7

37. Characteristics of Similar Solids For similar solids, the corresponding lengths are proportional, and the corresponding faces are similar.

38. Theorem 12-15 If two solids are similar with a scale factor of a:b, then the surface areas have a ratio of a2:b2 and the volumes have a ratio of a3:b3