2. Geometric Solids

3. Use the following key for the formulas in this presentation. b = based = diameter h = heightr = radius l = lengthpi = 3.14 w = width l = slant height

4. Cylinder The cylinder has two circular bases. h r

5. Cylinder Volume = (pi)r 2 h h r

6. Cylinder SA = 2(pi)rh +2(pi)r 2 h r

7. Cone The cone consist of one circular base. l h r

8. Cone Volume = 1/3(pi)r 2 h l h r

9. Cone SA = (pi)rl + (pi)r 2 l h r

10. Sphere r V = (4/3)(pi)r 3

11. Sphere r SA = 4(pi)r 2

12. Rectangular Prism The Rectangular Prism has two rectangular bases. w h l

13. Rectangular Prism V = lwh w h l

14. Rectangular Prism SA = 2(lw + hw + lh) w h l

15. Square Pyramid The Square Pryamid has one square base. l l h w

16. Square Pyramid V = (1/3)lwh l l h w

17. Square Pyramid SA = 2ll + l 2 l l h w

18. Example Problems

19. Find the volume of the cylinder. 10 in 6 in

20. Find the volume of the cylinder. V = (pi) r 2 h 10 in 6 in

21. Find the volume of the cylinder. V = (pi) r 2 h pi = 3.14 r = 6 h = 10 10 in 6 in

22. Find the volume of the cylinder. V = (pi) r 2 h pi = 3.14 r = 6 h = 10 V = (3.14)(6 2 )(10) 10 in 6 in

23. Find the volume of the cylinder. V = (pi) r 2 h pi = 3.14 r = 6 h = 10 V = (3.14)(6 2 )(10) V = 1130.4 in 3 10 in 6 in

24. Find the surface area of the sphere. 14 cm

25. Find the surface area of the sphere. SA = 4 (pi) r 2 14 cm

26. Find the surface area of the sphere. SA = 4 (pi) r 2 pi = 3.14 diameter = 14 so… r = 7 14 cm

27. Find the surface area of the sphere. SA = 4 (pi) r 2 pi = 3.14 diameter = 14 so… r = 7 SA = 4(3.14)(7 2 ) 14 cm

28. Find the surface area of the sphere. SA = 4 (pi) r 2 pi = 3.14 diameter = 14 so… r = 7 SA = 4(3.14)(7 2 ) SA = 615.4 cm 2 14 cm

29. Find the volume of the prism. 1 ft 4 in 8 in

30. Find the volume of the prism. V = lwh 1 ft 4 in 8 in

31. Find the volume of the prism. V = lwh l = 8 in w = 4 in h = 1 ft = 12 in 1 ft 4 in 8 in

32. Find the volume of the prism. V = lwh l = 8 in w = 4 in h = 1 ft = 12 in V = (8)(4)(12) 1 ft 4 in 8 in

33. Find the volume of the prism. V = lwh l = 8 in w = 4 in h = 1 ft = 12 in V = (8)(4)(12) V = 384 in 3 1 ft 4 in 8 in

34. r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman?

35. r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Volume of top: (4/3)(3.14)(.7 3 ) = 1.4 ft 3

36. r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Volume of middle: (4/3)(3.14)(1 3 ) = 4.2 ft 3

37. r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Volume of bottom: (4/3)(3.14)(1.8 3 ) = 24.4 ft 3

38. r=8 in r= 1 ft r= 1.8 ft How much snow did it take to make the snowman? Total Volume: 1.4 + 4.2 + 24.4 = 30 ft 3

39. Created by: Lisa Alcott Lisa_Alcott@pinellas.k12kfl.us