1. Chapter 12 – Surface Area and Volume of Solids
REVIEW
Section 12.1– Space Figures and Nets

2. Section 12.1
Polyhedron – a 3-D figure whose surfaces are polygons.
Face – individual polygon of the polyhedron.
Edge – is a segment that is formed by the intersection of two faces.
Vertex – is a point where three or more edges intersect.
REVIEW

3. Section 12.1
Net – a 2-D pattern that you can fold to form a 3-D figure.
Euler’s Formula – the number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula:
F + V = E + 2
REVIEW

4. CUBE: Net Drawing
REVIEW

5. CUBE: 3-Dimensional
Faces
REVIEW
Edge
Vertex

6. CYLINDER: Net Drawing
REVIEW

7. CYLINDER: 3-Dimensional
Faces
REVIEW
Edge

8. TRIANGULAR PRISM: Net Drawing
REVIEW

9. TRIANGULAR PRISM: 3-Dimensional
REVIEW
Edge
Faces
Vertex

10. RECTANGULAR PRISM: Net Drawing
REVIEW

11. RECTANGULAR PRISM: 3-Dimensional
Faces
REVIEW
Edge
Vertex

12. HEXAGONAL PRISM: Net Drawing
REVIEW

13. HEXAGONAL PRISM: 3-Dimensional
Faces
REVIEW
Edge
Vertex

14. TRIANGULAR PYRAMID: Net Drawing
REVIEW

15. TRIANGULAR PYRAMID: 3-Dimensional
REVIEW
Slant Height
Altitude

16. SQUARE PYRAMID: Net Drawing
Slant Height
REVIEW

17. SQUARE PYRAMID: 3-Dimensional
Slant Height
REVIEW

18. HEXAGONAL PYRAMID: Net Drawing
REVIEW

19. HEXAGONAL PYRAMID: 3-Dimensional
Slant Height
REVIEW
Altitude

20. Chapter 12 – Surface Area and Volume of Solids
Section 12.2 – Surface Areas of Prisms and Cylinders

21. Section 12.2
Prism – is a polyhedron with exactly two congruent, parallel faces.
Bases – two congruent, parallel faces of a prism.
Lateral Faces – additional faces of a prism.
Altitude – is a perpendicular segment that joins the planes of the bases.

22. Section 12.2 Height – the length of the altitude.
Right Prism – the lateral faces are rectangles and a lateral edge is the altitude of the prism.
Oblique Prism – at least one lateral face is not a rectangle.
Lateral Area – is the sum of the area of the lateral faces.

23. CUBE: 3-Dimensional
BASE
LATERAL
FACE

24. RECTANGULAR PRISM: 3-Dimensional
BASE
LATERAL
FACE

25. TRIANGULAR PRISM: 3-Dimensional
LATERAL
FACE
BASE

26. HEXAGONAL PRISM: 3-Dimensional
BASE
LATERAL
FACE

27. OBLIQUE PRISM: 3-Dimensional
BASE
LATERAL
FACE
ALTITUDE

28. Section 12.2
Surface Area – the sum of the lateral area and the two bases.
Theorem 10-1 – the lateral area of a right prism is the product of the perimeter of the base and the height. L.A. = ph The surface area of a right prism is the sum of the lateral area and the area of the 2 bases. S.A. = L.A. + 2B

29. Section 12.2
Cylinder – is a three-dimensional figure with exactly two congruent, parallel faces.
Bases – two congruent, parallel faces of a cylinder are circles.
Altitude – is a perpendicular segment that joins the planes of the bases.

30. CYLINDER: 3-Dimensional
BASE

31. OBLIQUE CYLINDER: 3-Dimensional
BASE
ALTITUDE

32. Section 12.2
Surface Area – the sum of the lateral area and the two circular bases.
Theorem – the lateral area of a right prism is the product of the circumference of the base and the height of the cylinder.
L.A. = 2πrh or L.A. = πdh
The surface area of a right prism is the sum of the lateral area and the area of the 2 bases.
S.A. = L.A. + 2B or S.A. = 2πrh + 2πr2

33. Chapter 12 – Surface Area and Volume of Solids
Section 12.3 – Surface Areas and Pyramids and Cones

34. Moving from Prisms/Cylinders to Pyramids/Cones

35. Section 12.3
Pyramid – is a polyhedron in which one face can be any polygon and the other faces are triangles that meet at a common vertex.
Bases – the only face of a pyramid that is not a triangle.
Lateral Faces – triangles of pyramid.
Vertex of a pyramid – the point where all lateral faces of a pyramid meet.

36. Section 12.3
Altitude – is a perpendicular segment from the vertex to the plane of the base.
Height – the length of the altitude (h).
Regular Pyramid – a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.
Slant Height – is the length of the altitude of a lateral face of a pyramid.
Lateral Area – is the sum of the area of the congruent lateral faces.

37. TRIANGULAR PYRAMID: 3-Dimensional
Slant Height
Altitude

38. SQUARE PYRAMID: 3-Dimensional
Slant Height

39. HEXAGONAL PYRAMID: 3-Dimensional
Slant Height
Altitude

40. Section 12.3
Surface Area – the sum of the lateral area and the area of the base.
Theorem – the lateral area of a regular pyramid is the half the product of the perimeter of the base and the slant height. L.A. = ½ pl The surface area of a regular pyramid is the sum of the lateral area and the area of the base. S.A. = L.A. + B

41. Section 12.3
Cone – is a “pointed” like a pyramid, but its base is a circle.
Right Cone – the altitude is a perpendicular segment from the vertex to the center of the base.
Bases – the only circle on a cone.
Vertex of a cone – the only distinctive point on the object.

42. Section 12.3
Altitude – is a perpendicular segment from the vertex to the plane of the base.
Height – the length of the altitude (h).
Slant Height – is the distance from the vertex to a point on the edge of the base.
Lateral Area – is ½ the perimeter (circumference) of the base times the slant height.

43. CONE: Net Drawing

44. CONE: 3-Dimensional

45. Section 12.3
Surface Area – the sum of the lateral area and the area of the base.
Theorem – the lateral area of a right cone is the half the product of the circumference of the base and the slant height. L.A. = ½ 2rl or rl
The surface area of a right cone is the sum of the lateral area and the area of the base. S.A. = L.A. + B

46. Chapter 12 – Surface Area and Volume
Section 12.6 – Surface Area and Volumes of Spheres

47. Section 12.6 Sphere Set of all points equidistant from a given point.

48. Section 12.6
Surface Area of a Sphere
S = 4πr 2 C