1. Copyright © Ed2Net Learning, Inc.1 Three-Dimensional Figures Grade 5

2. Copyright © Ed2Net Learning, Inc. 2 Warm Up Multiply. Round to the nearest tenth. 1. 8.2 x 4.8 x 2.1 2. 5.9 x 1.0 x 7.3 3. 1.0 x 0.9 x 1.3

3. Copyright © Ed2Net Learning, Inc. 3 Three-Dimensional Figures Most common shapes are three-dimensional figures. They have length, width, and depth (or height). You can describe a 3-dimesional figure by its parts.  A face is a flat side.  A base is a face on which the figure sits.  An edge is where 2 faces meet.  A vertex is where 3 or more faces meet.

4. Copyright © Ed2Net Learning, Inc. 4 Three-Dimensional Figures A face is a flat surface. The sides are called lateral faces. The edges intersect at the vertices. The edges are the segments formed by the intersecting faces. Dashed Lines are used to indicate edges that are hidden from view.

5. Copyright © Ed2Net Learning, Inc. 5 Prism Has at least three lateral faces that are rectangles The top and bottom faces are the bases and are parallel The shape of the base tells the name of the prism. Rectangular PrismTriangular PrismSquare Prism or Cube

6. Copyright © Ed2Net Learning, Inc. 6 Pyramid Has at least three lateral faces that are triangles and only one base. The base can be shaped like any closed figure with three or more sides. The shape of the base tells the name of the pyramid. Triangular Pyramid Square Pyramid

7. Copyright © Ed2Net Learning, Inc. 7 Cone Has only one base The base is a circle Has one vertex and no edges.

8. Copyright © Ed2Net Learning, Inc. 8 Cylinder Has only two bases The bases are circles Has no vertices and no edges

9. Copyright © Ed2Net Learning, Inc. 9 Sphere All of the points on a sphere are the same distance from the center. No faces, bases, edges, or vertices. center

10. Copyright © Ed2Net Learning, Inc. 10 Identify Three-Dimensional Figure One circular base No edge No vertex The figure is a cone.

11. Copyright © Ed2Net Learning, Inc. 11 Try This! Identify the figure.

12. Copyright © Ed2Net Learning, Inc. 12 Try This! Determine the number of vertices.

13. Copyright © Ed2Net Learning, Inc. 13 Plane A plane is a flat surface with no thickness. It contains many lines and extends without end in the directions of all its lines.  Example: ABCD or M The faces of a prism are parts of a plane. M A B C D

14. Copyright © Ed2Net Learning, Inc. 14 Parallel and Skew Lines Two lines intersect if they have exactly one point in common. Two lines that lie in the same plane and do not intersect are parallel.  Segments and rays are parallel if they lie in parallel lines.  PS QR Skew lines are lines that do not lie in the same plane.  They are not parallel and they do not intersect.  Skew segments must be parts of skew lines.  PS and RV are skew. R V W S Q U P T

15. Copyright © Ed2Net Learning, Inc. 15 Your Turn! Identify two planes in the rectangular prism. (Three vertices are needed to name a plane). Name two other pairs of lines that are skew lines. R V W S Q U P T

16. Copyright © Ed2Net Learning, Inc. 16 Volume of Rectangular Prisms The volume of a solid is the amount of space it contains.  Volume is measured in cubic units, such as cubic feet (ft3) and cubic meters (m3).  This tells you the number of cubes of a given size it will take to fill the prism. Prism

17. Copyright © Ed2Net Learning, Inc. 17 Volume of Rectangular Prisms The volume V of a rectangular prism is the product of the length, width, and height. V = lwh h w l

18. Copyright © Ed2Net Learning, Inc. 18 Volume of Rectangular Prisms The volume V of a rectangular prism is also the product of the area of base (B) by the height. V = Bh B h Volume of the base or the number of cubes needed to cover the base Number of rows of cubes needed to fill the prism

19. Copyright © Ed2Net Learning, Inc. 19 Example Find the volume of the rectangular prism. Method 1 V=lwh = 12 x 10 x 6 V = 720 cm 3 Method 2 V=Bh B = 12 x 10 = 120 V = Bh = 120 x 6 = 720 cm 3 6 cm 10 cm 12 cm

20. Copyright © Ed2Net Learning, Inc. 20 Your Turn! Find the volume of each rectangular prism. 10 in 6 in 4 in

21. Copyright © Ed2Net Learning, Inc. 21 Surface Area of Rectangular Prisms The surface area of a solid is the sum of the areas of its outside surfaces. Rectangular Prism Unfold.Net The two-dimensional representation of a solid is called a net. The surface area of a rectangular prism is equal to the area of its net.

22. Copyright © Ed2Net Learning, Inc. 22 Finding Surface Area Using a Net EXAMPLE 1 Find the surface area of the rectangular prism. Surface Area of Rectangular Prisms 1 Find the area of each face. Area of top or bottom: 6  4 = 24 Area of front or back: 6  3 = 18 Area of either side: 4  3 = 12 2 Add the areas of all six faces. 24 + 24 + 18 + 18 + 12 + 12 = 108 ANSWER The surface area of the prism is 108 square inches.

23. Copyright © Ed2Net Learning, Inc. 23 Surface Area of Rectangular Prisms NOTE BOOK Words The surface area S of a rectangular prism is the sum of the areas of its faces. Algebra S = 2 l w + 2 l h + 2 w h Surface Area of a Rectangular Prism h w l

24. Copyright © Ed2Net Learning, Inc. 24 Surface Area of Rectangular Prisms Finding Surface Area Using a Formula EXAMPLE 2 Find the surface area of the rectangular prism. ANSWER The surface area of the prism is 230 square meters. S = 2 l w + 2 l h + 2 w h = 2(15)(2) + 2(15)(5) + 2(2)(5) = 60 + 150 + 20 = 230 15 m 5 m 2 m Write formula for surface area. Substitute 15 for l, 2 for w, and 5 for h. Multiply. Add.

25. Copyright © Ed2Net Learning, Inc. 25 Your Turn! Find the surface area of the rectangular prism. 5 cm 10 cm

26. Copyright © Ed2Net Learning, Inc. 26 Activity You can make a model to find the surface area of a cylinder. Surface Area of Cylinders 1 2 3 Cut out pieces of paper to cover a cylindrical can. What shape are the pieces of paper that cover the top and bottom of the can? What shape is the piece of paper that covers the side of the can? Describe the relationship between the length of the paper used to cover the side of the can and the circumference of the paper used to cover the top of the can. Use your pieces of paper to find the surface area of the can.

27. Copyright © Ed2Net Learning, Inc. 27 Surface Area of Cylinders In the previous slide, you saw that the net of a cylinder consists of two circles that form the bases and a rectangle that forms the curved surface of the cylinder. The circumference of a base, 2  r, is equal to the length of the rectangle, and the height of the cylinder is the width of the rectangle. CylinderUnfoldNet

28. Copyright © Ed2Net Learning, Inc. 28 NOTE BOOK Words The surface area S of a cylinder is the sum of the area of the curved surface and the areas of the circular bases. Algebra S = 2  r h + 2  r 2 Surface Area of Cylinders

29. Copyright © Ed2Net Learning, Inc. 29 Finding the Surface Area of a Cylinder EXAMPLE 1 Find the surface area of the cylinder. Use 3.14 for . Surface Area of Cylinders S = 2  r h + 2  r 2  2(3.14) (3) (8) + 2(3.14) (3) 2 = 150.72 + 56.52  207 ANSWER The surface area is about 207 square centimeters. Write formula. Substitute values. Multiply. Add.

30. Copyright © Ed2Net Learning, Inc. 30 Your Turn! Find the surface area of the cylinder. Use 3.14 for π. 3 mm 5 mm

31. Copyright © Ed2Net Learning, Inc. 31 Let us take a Break!

32. Copyright © Ed2Net Learning, Inc. 32

33. Copyright © Ed2Net Learning, Inc. 33 Critical Thinking If all the dimensions of a rectangular prism are doubled, does the volume double? Explain.

34. Copyright © Ed2Net Learning, Inc. 34 Assessment Identify each figure. (1) (2) (3)

35. Copyright © Ed2Net Learning, Inc. 35 Assessment Find the volume of each figure. Round to the nearest tenth if necessary. (4) (5) (6) 4 yd 8 yd 3 yd 9 3/8 ft 5 ½ ft 2 ft 5 in. 4 in. 8 in.

36. Copyright © Ed2Net Learning, Inc. 36 Assessment Find the surface area of each rectangular prism. Round to the nearest tenth if necessary. (7) (8) (9) 7 in. 6 in. 5.9 cm 6.8 cm 4.5 cm 5 in. 4 in. 8 in.

37. Copyright © Ed2Net Learning, Inc. 37 Assessment Find the surface area of each cylinder. Round to the nearest tenth. Use 3.14 for π. 2 ft 5 ft 4 in. 6 in. 2 cm 10 cm (10) (11) (12)

38. Copyright © Ed2Net Learning, Inc. 38 Review Common Three-Dimensional Figures:  Prism  Pyramid  Cone  Cylinder  Sphere Skew lines are lines that do not lie in the same plane. Volume of rectangular prism V=lwh = Bh Surface Area of rectangular prism S = 2 lw + 2 lh + 2 wh Surface Area of cylinder S = 2  r h + 2  r 2

39. Copyright © Ed2Net Learning, Inc. 39 Thank You! Remember to do the practice worksheets!!!