11.1 Three-Dimensional Figures

1. 11.1 Three-Dimensional Figures Vocabulary Plane – A two-dimensional flat surface that extends in all directions Solid – Intersecting plans that form three – dimensional figures. Polyhedron – a solid with flat surfaces Edge – where two plans intersect in a line Vertex – where three or more planes intersect in a point

2. Vocabulary Cont. Face – a flat surface Prism – a polyhedron with two parallel, congruent faces called bases. Base – in a prism, any two parallel congruent faces Pyramid – a polyhedron with one base that is any polygon. Skew lines – lines that are neither intersecting nor parallel. They lie in different planes

3. Identifying solids

4. Naming bases, faces, edges, and vertices Faces: EFGH, HGLM, HMJE, FGLK, KLMJ, EFKJ, Edge: FG, GH, HE, EF, FK, GL, HM, EJ, JK, KL. LM, MJ Vertices: F, G, H, E, L, M, J, K

5. Edges that are SKEW to FM will not have the vertices F or M. When a diagonal (FM) is drawn through a prism, you can determine SKEW lines. Examples: GL, KL, KJ, EH, GH, and EJ are Skew to FM.

6. Identify the solid. Name the bases, faces, edges, and faces. Faces: QPNM, LKJH, QPKL, NPKJ, NJHM, MHLQ Edge: QP, PN, NM, MQ,QL,PK, NJ, MH, JK, KL. LH, HJ Vertices: Q, P, N, M, H, L, K, J

7. Name the Diagonal and name all segments that are skew to it. DIAGONAL IS PH Skew segments: QM, MN, QL, LK, KJ, and NJ are Skew to PH.

8. 11.2 Volume Vocabulary Volume- the measure of space occupied by a solid region Cylinder- a solid whose bases are congruent, parallel circles connected with a curved side.

9. Volume Formula Volume = area of the base x height V = Bh

10. Find the volume of the prism

11. Find the volume of the prism

12. Find the volume of the Cylinder

14. 11.3Volume of Pyramids and Cones Vocabulary Cone- A three-dimensional figure with one circular base.

15. Formula Volume = 1/3 x area of the base x height

16. Find the Volume of the Pyramid

17. Find the Volume

18. Find the Volume of the Cone

19. Find the Volume

20. Find the Volume

21. 11.4 Surface area Vocabulary Surface Area - Surface area is the sum of the area of all the surfaces, or faces of a three dimensional figure.

22. Method One: Add up the area of each face This prism has 3 sets of congruent faces: Top and bottom Front and back Side and side Top and bottom = 15 x 10 = 150 Front and Back = 15 x 6 = 90 Side and Side = 6 x 10 = 60 Surface area = 2(150) + 2(90) + 2(60) Surface area = 600 cm2

23. REMINDER!! The base of a triangular prism is a TRIANGLE!! Top base and bottom base = ½ x 3 x 4 = 6 Back = 3 x 8 = 24 Top= 8 x 5 = 40 Bottom = 4 x 8 = 32 Surface area = 2(6) + 24 + 40 + 32 = 108 Surface area = 108 in2

24. Method 2Surface area formula

25. S = 2B + Ch S = 2B +Ph Base = 9 x 4 = 36 Perimeter = 9 + 4 + 9 + 4 = 26 Height = 5 S = 2(36) + 26(5) Surface area = 202 in2

26. S = 2B + Ph REMINDER!! The base of a triangular prism is a TRIANGLE!! S = 2B +Ph Base = ½ x 12 x 8 = 48 Perimeter = 12 + 10 + 10 = 32 Height = 15 S = 2(48) + 32(15) Surface area = 576 m2

27. Surface area of Cylinders The area of the rectangular area is found using the height of the cylinder and the circumference of the circle The surface are of a Cylinder is made up of 2 circles and a rectangle

28. Formula

29. S = 2B + Ch S = 2B +Ch Base = = x 3.52 ≈ 36.48 Circumference = = 2 x x 3.5 ≈ 21.99 Height = 0.6 S = 2(36.32) + 21.99(0.6) Surface area ≈ 85.83 m2 Your answer might be different depending on your rounding

30. You Try! ANSWER: ≈ 894.73

31. 11.5 Surface area of Pyramids and Cones Vocabulary Lateral Face- the sides of a pyramid Slant Height - The altitude or height of each lateral face Lateral area – The sum of the area of the lateral faces of a pyramid

32. Find the surface area

33. Find surface area of the Pyramid

34. Find surface area of the Pyramid

35. Find the Surface Area of a Cone

36. Find the surface are of the Cone

37. Find the Surface Area

38. 11-6 Similar Solids Vocabulary Similar Figures: solids which have the same shape and their corresponding linear measures are proportional.

41. If you know two figures are similar, you can find missing measures by setting up and solving a proportion.

46. 11-7 Precision and Significant Digits Vocabulary Precision: The exactness to which a measurement is made. Significant digits: The digits you record when you measure and use all of the digits that are actually measured plus one estimated digit.

47. If a number contains a decimal point, the number of significant digits is found by counting the digits from left to right, starting with the first nonzero digit and ending with the last digit. If a number does not contain a decimal point, the number of significant digits is found by counting from left to right, starting with the first digit and ending with the last non zero digit.

48. Determining Significant digits If a number contains a decimal point, the number of significant digits is found by counting the digits from left to right, starting with the first nonzero digit and ending with the last digit. If a number does not contain a decimal point, the number of significant digits is found by counting from left to right, starting with the first digit and ending with the last non zero digit.

50. When adding or subtracting measurements, the sum or difference should have the same precision as the least precise measurement When multiplying or dividing measurements, the product or quotient should have the same number of significant digits as the measurement with the least number of significant digits.