1. Solid Geometry

2. Three Dimensions
Solid Geometry is the geometry of three-dimensional space
It is called three-dimensional, or 3D because there are three dimensions: width, depth and height.

3. Polyhedron A geometric object with flat faces and straight edges.
each face is a polygon.

4. Polyhedron FACE: Polygon shaped sides of a polyhedron
EDGE: Line segment formed by intersection of two faces
VERTEX: Point where three or more edges meet

5. Base The surface that a solid object stands on
or the bottom line of a shape such as a triangle or rectangle.

6. Polyhedron
Just like a 2D polygon a Polyhedron can be regular

7. Polyhedron
…or Irregular

8. Polyhedron
A Polyhedron can also be semi-Regular

9. Polyhedron
Just like a 2D polygon, a polyhedron can be convex

10. Polyhedron
…or concave

11. Prism A solid object that has two identical bases and all flat sides.
The shape of the bases give the prism it’s name
"triangular prism“
It is a polyhedron.

12. Pyramid
A solid object where: * The base is a polygon (a straight-sided shape) * The sides are triangles which meet at the top (the apex). It is a polyhedron.

13. Cylinder A cylinder is a solid object with:
* two identical flat circular (or elliptical) ends
* and one curved side.

14. Cone A solid (3-dimensional) object that has a circular base
and one vertex

15. Sphere
A solid
(3-dimensional) object that has one curved side

16. Prisms & Pyramids Triangular Prism Rectangular Prism Cube
Type
Examples
Properties
Triangular Prism
● 5 faces
2 triangular bases
3 rectangular faces
● 9 edges
● 6 vertices
Rectangular Prism
6 faces
2 rectangular bases
4 rectangular faces
● 12 edges
● 8 vertices
Cube
● 6 faces
2 square bases
4 square faces
Square Pyramid
1 square base
4 triangular faces
● 8 edges
● 5 vertices
Triangular Pyramid
● 4 faces
1 triangular base
3 triangular faces
● 6 edges
● 4 vertices

17. Three Dimensional Figures with Curved Surfaces
Type
Example
Properties
Cylinder
● 2 circular bases
● 1 curved surface
Cone
● 1 circular base
● 1 vertex
Sphere

18. VOLUME

19. Prism
V=Bh
B: Area of the base
h: height/length of the prism

20. Prism V=Bh V= (Area of Triangle) * h V= (½bh) * h V= (½*19*24) *47
V= 10,716 cm3

21. Prism V=Bh V= (Area of Rect.) * h V= (bh) * h V= (2 * 3) * 6 V=(6) * 6
V= 36 ft3

22. Cylinder
V=Bh
B: Area of the base
h: height/length of the prism

23. Cylinder V=Bh V= (Area of Circle) * h V= (πr2) * h V= (π * 32) *10
V= cm3

24. Cylinder V=Bh V= (Area of Circle) * h V= (πr2) * h V= (π * 52) *21
V= 1,648.5 ft3

25. Pyramid
V=1/3Bh
B: Area of the base
h: height/length of the prism

26. Pyramid V=1/3Bh V= 1/3(Area of Tri.) * h V= 1/3 * (½bh) * h
V= 20 cm3

27. Pyramid V=1/3Bh V= 1/3(Area of Sq.) * h V= 1/3 * (b * h) * h
V= 250/3 units3

28. Cone
V=1/3Bh
B: Area of the base
h: height/length of the prism

29. Cone V=1/3Bh V= 1/3(Area of Circle)* h V= 1/3(πr2) * h
V= in3

30. Cone V=1/3Bh V= 1/3(Area of Circle)* h V= 1/3(πr2) * h
V= 1, cm3

31. Sphere
V=4/3 πr3

32. Sphere V=4/3 πr3 V= 4/3 πr3 V= 4/3 * π * 143 V= 4/3 * π * 2744
V= 11, cm3

33. Sphere V=4/3 πr3 V= 4/3 πr3 V= 4/3 * π * 33 V= 4/3 * π * 27
V= cm3

34. SURFACE AREA

35. Surface Area
The sum of the area of the bases and lateral surfaces

36. Right Prism SA=2B+Ph B: Area of the base P: Perimeter of a base
h: height/length of the prism

37. Right Prism SA=2B+Ph SA=2(Area of Rect.)+Ph SA= 2(bh) + Ph
SA= 62 cm2

38. Right Prism SA=2B+Ph SA=2(Area of Tri.)+Ph SA= 2(1/2bh) + Ph
(3+8+√73)7
SA=2(12) + (11+√73)5
SA= √73
SA= √73 m2
SA = m2
SA=2B+Ph

39. Right Cylinder SA=2B+Ch B: Area of the base C: Circumference of a base
h: height/length of the cylinder

40. Right Cylinder SA=2B+Ch SA=2(Area of Circ.)+Ch SA= 2(πr2) + (2πr)h
SA= cm2

41. Right Cylinder SA=2B+Ch SA=2(Area of Circ.)+Ch SA= 2(πr2) + (2πr)h
SA= cm2

42. Right Pyramid SA=B + ½Ps B: Area of the base P: Perimeter of a base
s: slant height of the lateral side

43. Right Pyramid (& Cone)
What is “slant height”?

44. Right Pyramid SA=B + ½Ps SA=(Area of Rect.)+½Ps SA= (bh) + ½Ps
SA= units2

45. Right Pyramid SA=B + ½Ps SA=(Area of Rect.)+½Ps SA= (bh) + ½Ps
SA= 602 in2
10 in

46. Right Cone SA=B + ½Cs B: Area of the base P: Circumference of a base
s: slant height of the lateral side

47. Right Cone SA=B + ½Cs SA=(Area of Circ.)+½Cs SA= (πr2) + ½(2πr)s
SA= in2

48. Right Cone SA=B + ½Cs SA=(Area of Circ.)+½Cs SA= (πr2) + ½(2πr)s
SA= 4.9 ft2

49. Sphere
SA=4πr2
r: radius

50. Sphere SA=4πr2 SA= 4πr2 SA= 4*π*42 SA= 4*π*16 SA= 64π
SA= units2

51. Sphere SA=4πr2 SA= 4πr2 SA= 4*π*322 SA= 4*π*1024 SA= 4096π
SA= 12, units2