The Amazing World of 3-D

1. The Amazing World of 3-D By: Tony Shindeldecker Click to Start

2. The purpose of this slideshow is to: • reinforce the topics covered in class including 3-D figures, volumes, and surface areas • Help you to practice some word problems before the upcoming test Click to Continue

3. After this slide show you should be able to: • identify the major characteristics of a cylinder, cone, pyramid, and sphere • Using the formulas for the volume and surface area of each figure, solve some real world problems involving 3-D figures Click to Continue

4. WHY study geometry??? Suppose you have a new bedroom and need to paint your room a new bright red instead of the old yellow paint. How do you know how much paint to buy when you go to the store?? Amazingly the answer is found in GEOMETRY!! Click to Continue

5. Careers that involve Geometry: • Architecture • Video Game Programmer • Computer Aided Design • Software Engineer • Astronomer • Robotics …and many, many more! Click HERE to Continue

6. How do I navigate? Click on the following buttons to : Go to the next slide Go back a slide Go to the previous slide viewed Go to the table of contents

7. Table of Contents: 2-D vs. 3-D objects Learn about 3-D Figures Volume and Surface Area Cube Sphere Cylinder Cone Pyramid Quiz

8. 2-Dimensional Objects - 2-Dimensional objects have length and width, but NOdepth

9. 3-Dimensional Objects - 3-Dimensional objects have length, width, ANDdepth

10. - In this lesson we will be focusing on 3-Dimensional objects To learn about 3-D objects and figures Click Here

11. Let’s Learn About 3-D Figures!!!

12. First we need to understand some terms: Volume: the amount of space occupied by a 3-D figure or region of space Example: how much milk is poured into a glass

13. Surface Area:the total area of all the faces of a 3- Dimensional figure Example: how much leather is used to create a soccer ball

14. - Now that you know what volume and surface area are, it’s time to learn about some 3-D figures! To learn about Cubes Click Here!

15. Cube A Cube is a 3-Dimensional Figure having six matching sides

16. Cube Volume: V = L3 Volume = (length of one of it’s sides)3 = (L x L x L) Surface Area: S = 6 ( L x L) Surface Area = 6 times the area of one of it’s sides

17. What is the volume? What is the surface area? Practice: An ice cube has 6 equal sides and the length of one of its sides is 4 cm * Try each problem on scrap paper, then click to reveal the answer when you are ready

18. What is the volume of the ice cube? Given: L = 4 cm Remember: V = L3 Answer: Click Answer to reveal answer

19. What is the volume of the ice cube? Given: L = 4 cm Remember: V = L3 Answer: V = (4 cm)3 Volume = 64 cm3

20. What is the surface area of the ice cube? Given: L = 4 cm Remember: S = 6(L x L) Answer: Click Answer to reveal answer

21. What is the surface area of the ice cube? Given: L = 4 cm Remember: S = 6(L x L) Answer: S = 6(4 cm x 4 cm) S = 6(16 cm2) Surface Area = 96 cm2

22. You should now have a good understanding of: • The major characteristics of a cube • How to calculate the volume and surface area of a cube To learn about spheres Click Here!

23. Sphere A Sphere is a 3-Dimensional Figure with all of it’s points the same distance from it’s center point

24. Sphere Volume: V = 4/3 x p x r3 Volume = 4/3 x pi x (radius)3 * where r is the radius of the sphere * Surface Area: S = 4 x p x r2 Surface Area = 4 x pi x (radius)2

25. What is the volume? What is the surface area? Practice: You just bought a brand new volleyball and it has a radius of 0.4 ft * Try each problem on scrap paper, then click to reveal the answer when you are ready

26. What is the volume of the volleyball? Given: r = 0.4 ft Remember: V = 4/3 x p x r3 Answer: Click Answer to reveal answer

27. What is the volume of the volleyball? Given: r = 0.4 ft Remember: V = 4/3 x p x r3 Answer: V = 4/3 x p x (0.4 ft)3 V = 4/3 x p x (0.064 ft3) Volume = 0.268 ft3

28. What is the surface area of the volleyball? Given: r = 0.4 ft Remember: S = 4 x p x r2 Answer: Click Answer to reveal answer

29. What is the surface area of the volleyball? Given: r = 0.4 ft Remember: S = 4 x p x r2 Answer: S = 4 x p x (0.4 ft)2 S = 4 x p x (0.16 ft2) Surface Area = 2.01 ft3

30. You should now have a good understanding of: • The major characteristics of a sphere • How to calculate the volume and surface area of a sphere To learn about cylinders Click Here!

31. Cylinder A Cylinder is a 3-Dimensional Figure having two equal circular bases that are parallel

32. Cylinder Volume: V = h x p x r2 Volume = height x pi x (radius)2 * where h is the height of the cylinder * Surface Area: S = 2prh + 2pr2 Surface Area = (2 x p x r x h) + (2 x p x r2)

33. What is the volume? What is the surface area? Practice: A can of your favorite pop has a height of 4 in. and the radius of one of the bases is 3 in. * Try each problem on scrap paper, then click to reveal the answer when you are ready

34. What is the volume of the pop can? Given: radius of base = 3 in height of cylinder = 4 in Remember: V = h x p x r2 Answer: Click Answer to reveal answer

35. What is the volume of the pop can? Given: radius of base = 3 in height of cylinder = 4 in Remember: V = h x p x r2 Answer: V = 4 in x p x (3 in)2 V = 4 in x p x 9 in2 Volume = 113.1 in3

36. What is the surface area of the pop can? Given: r = 3 in h = 4 in Remember: S = 2prh + 2pr2 Answer: Click Answer to reveal answer

37. What is the surface area of the pop can? Given: r = 3 in h = 4 in Remember: S = 2prh + 2pr2 Answer: S = 2p(3in)(4in) + 2p(3 in)2 S = 2p(12 in2) + 2p(9 in2) Surface Area = 131.9 in2

38. You should now have a good understanding of: • The major characteristics of a cylinder • How to calculate the volume and surface area of a cylinder To learn about cones ClickHere!

39. Cone A Cone is a 3-Dimensional Figure having a circular base and a single vertex

40. Cone Volume: V = 1/3 x p x r2 x h Volume = 1/3 x pi x (radius)2 xheight where h is the height of the cone * * and r is the radius of the base of the cone

41. Practice: While driving for a Drivers Ed course you hit a cone marking a pothole. The height of the cone is 1 yd and the radius of the base is 0.25 yd What is the volume? * Try each problem on scrap paper, then click to reveal the answer when you are ready

42. What is the volume of the cone? Given: radius of base = 0.25 yd height of cone = 1 yd Remember: V = 1/3 x p x r2 xh Answer: Click Answer to reveal answer

43. What is the volume of the cone? Given: radius of base = 0.25 yd height of cone = 1 yd Remember: V = 1/3 x p x r2 xh Answer: V = 1/3 x p x (0.25 yd)2 x 1yd V = 1/3 x p x 0.0625 yd2 x 1yd Volume = 0.065 yd3

44. You should now have a good understanding of: • The major characteristics of a cone • How to calculate the volume of a cone To learn about pyramids ClickHere!

45. Pyramid A Pyramid is a 3-Dimensional Figure with a squarebase and 4triangle-shapedsides

46. Pyramid Volume: V = 1/3 x B x h Volume = 1/3 x area of the base xheight where h is the height of the pyramid * * and B is the area of the base of the pyramid

47. Practice: You decide to take a trip to Egypt and you visit the Great Pyramid of Giza. You learn that the height of the pyramid is 450 ft and the length and width of the base are both equal to 755 ft What is the volume? * Try each problem on scrap paper, then click to reveal the answer when you are ready

48. What is the volume of the pyramid? Given: l and w of base = 755 ft h = 450 ft Remember: V = 1/3 x B x h Answer: Click Answer to reveal answer

49. What is the volume of the pyramid? Given: l and w of base = 755 ft h = 450 ft Remember: V = 1/3 x B x h Answer: V = 1/3 x(755 ft x 755 ft) x 450 ft V = 1/3 x(570,025 ft2) x 450 ft Volume = 256,511,250 ft3

50. You should now have a good understanding of: • The major characteristics of a pyramid • How to calculate the volume of a pyramid To continue to the Quiz ClickHere!