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1. SURFACE AREA and VOLUME Solid Figures Introduction CYLINDERS PRISMS PYRAMIDS SPHERES CONES APPENDIX

2. SURFACE AREA and VOLUME SOLID FIGURES In a previous unit we discussed POLYGONS. POLYGONS are 2-dimensional objects. That means they have length and width, but no depth. Like they are cut out of paper. APPENDIX MENU

3. SURFACE AREA and VOLUME SOLID FIGURES In this unit, we will learn about SOLIDS. A SOLID is a 3-dimensional (3D) object. That means it has length, width AND depth. APPENDIX MENU

4. SURFACE AREA and VOLUME SOLID FIGURES When the SOLID is made up of POLYGONS, it is called a POLYHEDRON Each POLYHEDRON is made up of Surfaces (called faces) Segments (called edges) Corners (called vertices) APPENDIX MENU

5. SURFACE AREA and VOLUME SOLID FIGURES Before we can do anything with SOLIDS, we must understand the difference between these shapes There are many types of solids, we are going to study the 5 basic types: PRISM PYRAMID CYLINDER CONE SPHERE APPENDIX MENU

6. SURFACE AREA and VOLUME SOLID FIGURES To create a prism, draw any polygon you like. PRISMS: Next, draw another polygon, just like the first one Connect the corresponding vertices BASE BASE BASE APPENDIX MENU

7. SURFACE AREA and VOLUME SOLID FIGURES PRISMS: APPENDIX MENU

8. SURFACE AREA and VOLUME SOLID FIGURES PYRAMIDS: Pyramids have one base Instead of connecting to an identical base… They connect to a point. BASE BASE BASE APPENDIX MENU

9. SURFACE AREA and VOLUME SOLID FIGURES Pyramids: APPENDIX MENU

10. SURFACE AREA and VOLUME SOLID FIGURES When we name prisms and pyramids, we describe the base to tell what kind of prism or pyramid it is. APPENDIX MENU

11. SURFACE AREA and VOLUME SOLID FIGURES CYLINDERS: A cylinder is like a prism… But the bases are circles APPENDIX MENU

12. SURFACE AREA and VOLUME SOLID FIGURES Cylinders: APPENDIX MENU

13. SURFACE AREA and VOLUME SOLID FIGURES CONES: A cone is a circular pyramid. APPENDIX MENU

14. SURFACE AREA and VOLUME SOLID FIGURES Cones: APPENDIX MENU

15. SURFACE AREA and VOLUME SOLID FIGURES SPHERES: A sphere is a unique shape... It has no base or sides or edges or vertices. APPENDIX MENU

16. SURFACE AREA and VOLUME SOLID FIGURES SPHERES: APPENDIX MENU

17. SURFACE AREA and VOLUME SOLID FIGURES Identify each of the following shapes as a PRISM, PYRAMID, CYLINDER, CONE or SPHERE #1 #2 #3 #4 SPHERE CYLINDER PRISM #5 #6 PYRAMID #7 CYLINDER CONE PYRAMID #9 #10 #8 SPHERE CONE & SPHERE PRISM APPENDIX MENU

18. SURFACE AREA and VOLUME SOLID FIGURES So what are we going to do with these shapes? We are going to calculate SURFACE AREA and VOLUME APPENDIX MENU

19. SURFACE AREA and VOLUME SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU

20. SURFACE AREA and VOLUME SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU

21. SURFACE AREA and VOLUME SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU

22. SURFACE AREA and VOLUME SOLID FIGURES SUFARCE AREA: Is literally the area of all the surfaces of a solid. APPENDIX MENU

23. SURFACE AREA and VOLUME SOLID FIGURES VOLUME: Is the measure of how much “space” an object occupies. It is often thought of as how much water an object can hold. APPENDIX MENU

24. SURFACE AREA and VOLUME SOLID FIGURES VOLUME: Or how many cubic units it would take to fill an object This is why volume is measured in CUBIC UNITS Like: Cubic feet: ft3 Cubic centimeters cm3 APPENDIX MENU

25. SURFACE AREA and VOLUME PRISMS A prism is a solid with 2 congruent BASES connected by LATERAL FACES Lateral face APPENDIX MENU BASE

26. SURFACE AREA and VOLUME PRISMS To find the surface area of a PRISM, you can do it 2 ways: Method 1: Find the area of each shape that makes up the Solid, and add them together The front 2 x 10 = 20 12 The back 2 x 10 = 20 The left 6 x 10 = 60 10 60 The right 6 x 10 = 60 20 The top 2 x 6 = 12 The bottom 2 x 6 = 12 6 = 184 2 APPENDIX MENU

27. SURFACE AREA and VOLUME PRISMS To find the surface area of a PRISM, you can do it 2 ways: Method 2: Use the formula for SURFACE AREA: • Identify the BASEs (in a rectangular prism any pair of opposite sides can be bases) • Find the Area and Perimeter of the base BASE P; 16 A: 12 10 h: height of the prism B: area of the base 10 6 P: perimeter of the base 2 12 16 APPENDIX MENU

28. SURFACE AREA and VOLUME PRISMS Find the surface area of this regular decagonal prism: Find the perimeter of the base 6+6+6+6+6+6+6+6+6+6 =60 Area of the bases Lateral Area A: 270m2 P:60m 6m 4m APPENDIX MENU

29. SURFACE AREA and VOLUME PRISMS Finding Volume is easier! Find the VOLUME of this regular decagonal prism: h: height of the prism B: area of the base A: 270m2 P:60m 6m 4m APPENDIX MENU

30. SURFACE AREA and VOLUME PRISMS RIGHT PRISMS vs OBLIQUE PRISMS A right prism is a prism where the lateral faces are all perpendicular to the bases. An oblique prism is a prism where the lateral faces are NOT perpendicular to the bases. APPENDIX MENU

31. SURFACE AREA and VOLUME PRISMS SUMMARY: Things you need to know about a prism: A prism has 2 bases All the lateral faces are rectangles Surface Area = 2B + ph B is the area of the base p is the perimeter of the base h is the height of the prism p x h gives the lateral area Volume = B x h B is the area of the base h is the height of the prism APPENDIX MENU

32. SURFACE AREA and VOLUME PRISMS Find the… 3cm …Surface Area 4cm 2cm …Lateral Area First we have to find that missing side 3cm 4cm …Volume Use the Pythagorean theorem 5cm A: P: 6cm2 12cm APPENDIX MENU

33. SURFACE AREA and VOLUME PRISMS Find the… …Surface Area 3cm 4cm 5cm 2cm …Lateral Area …Volume A: P: 6cm2 12cm APPENDIX MENU

34. SURFACE AREA and VOLUME PRISMS Find the surface area and volume. 10 8 112 24 14 6 Area: Perimeter: 136ft2 52ft APPENDIX MENU

35. SURFACE AREA and VOLUME PRISMS Find the volume. APPENDIX MENU

36. SURFACE AREA and VOLUME PRISMS Archimedes problem. APPENDIX MENU

37. SURFACE AREA and VOLUME CYLINDERS Since CYLINDERS are like prisms with circular bases, We need to remember a few basic rules for circles. APPENDIX MENU

38. SURFACE AREA and VOLUME CYLINDERS Find the Circumference and area of the circle: 6in 12in The red segment is the DIAMETER We need the RADIUS APPENDIX MENU

39. SURFACE AREA and VOLUME CYLINDERS A CYLINDER is like a prism with circular bases The surface area of a cylinder can be found with this formula h: height of the cylinder B: area of the base Area of the bases Lateral Area C: circumference of the base Most people find this formula easier: APPENDIX MENU

40. SURFACE AREA and VOLUME CYLINDERS Find the SURFACE AREA of this cylinder: APPENDIX MENU

41. SURFACE AREA and VOLUME CYLINDERS The VOLUME of a Cylinder: The VOLUME of a cylinder can be found with this formula h: height of the cylinder B: area of the base The expanded version of the formula: APPENDIX MENU

42. SURFACE AREA and VOLUME CYLINDERS Find the VOLUME of this cylinder: APPENDIX MENU

43. SURFACE AREA and VOLUME CYLINDERS SUMMARY What you need to know about a cylinder: • A cylinder is a prism with circular bases • The lateral area is a rectangle • Surface Area: • Volume: • Lateral Area: APPENDIX MENU

44. SURFACE AREA and VOLUME CYLINDERS Find the Lateral Area, Surface Area and Volume: 11mm 9mm APPENDIX MENU

45. SURFACE AREA and VOLUME CYLINDERS Find the surface area and volume of this shape 31ft 8ft 16ft 31ft If it was a complete cylinder: What did we forget? But we only want half of it APPENDIX MENU

46. SURFACE AREA and VOLUME CYLINDERS Find the surface area and volume of this shape 31ft 8ft If it was a complete cylinder: But we only want half of it APPENDIX MENU

47. SURFACE AREA and VOLUME PYRAMIDS A PYRAMID is a shape with a single base, where all the vertices of the base are connected to a single point (apex) APPENDIX MENU

48. SURFACE AREA and VOLUME PYRAMIDS Just like with prisms, we will need to find: • Base Perimeter • Base Area • Height of the pyramid However, with pyramids, we will also need to find a different measurement… height Slant height …SLANT HEIGHT APPENDIX MENU

49. SURFACE AREA and VOLUME PYRAMIDS Slant height is the distance someone would travel walking up the OUTSIDE of a pyramid. SLANT HEIGHT APPENDIX MENU

50. SURFACE AREA and VOLUME PYRAMIDS APPENDIX MENU