1.3 Surface Areas of Objects Made from Right Rectangular and Triangular Prisms
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1 1.3 Surface Areas of Objects Made from Right Rectangular and Triangular Prisms
2 Important Vocabulary How many edges in a cube? How many faces in a cube? edge
3 Important Vocabulary cube Right Rectangular Prism
4 Investigation Each of you need 5 linking cubes. Assume each face of a linking cube has area 1 unit 2 What is the surface area of 1 cube? Put 2 cubes together to make a train. What is the surface area of the train? Place another cube at one end of your train. What is its surface area now? Continue to place cubes at one end of the train, and determine its surface area and complete the table. Number of Cubes 1 2 Total number of faces Surface Area 3 4 5
5 Investigation What patterns do you see in the table? What happens to the surface area each time you place another cube on the train? Explain why the surface area changes this way. Using 5 cubes, build an object that is different from the train and different from your partner s object. Sketch your object. Determine its surface area. Number of Cubes 1 Total number of faces Surface Area Compare the surface area of your object with that of your partner s object. Sketch your partner s object
6 Strategy for determining the surface area of the object 1. Count the square faces of all the cubes 2. subtract 2 faces for each surface where the cubes are joined. (We say the faces overlap) How many cubes? How many faces? How many faces overlap?
7 A COMPOSITE OBJECT Objects like these below are called composite objects because they are made up or are composed of, of other objects.
8 Determine the surface area of this composite object. Each cube has edge length 2 cm. 1. Count the square faces of all the cubes 2. subtract 2 faces for each surface where the cubes are joined. (We say the faces overlap) How many cubes? How many faces? How many faces overlap? The surface area is: 22 4 cm 2 = 88 cm 2
9 REVIEW: Determine the surface area of this right rectangular prism 7 cm 7 cm 3 cm 2 cm 3 cm 3 cm 2 cm 2 cm 7 cm The surface area is: 42 cm 2 +
10 Determine the surface area of this right rectangular prism 7 cm 7 cm 3 cm 2 cm 3 cm 3 cm 2 cm 2 cm 7 cm The surface area is: 42 cm cm 2 +
11 Determine the surface area of this right rectangular prism 7 cm 7 cm 3 cm 2 cm 3 cm 3 cm 2 cm 2 cm 7 cm The surface area is: 42 cm cm cm 2 =
12 Determine the surface area of this right rectangular prism 7 cm 7 cm 3 cm 2 cm 3 cm 3 cm 2 cm 2 cm 7 cm The surface area is: 42 cm cm cm 2 = 82 cm 2
13 Renee uses 3 pieces of foam to make this chair. Each piece of foam is a right rectangular prism with dimensions 60 cm by 20 cm by 20 cm. Can Renee cover the chair with 2 m 2 of fabric? Explain.
14 Renee uses 3 pieces of foam to make this chair. Each piece of foam is a right rectangular prism with dimensions 60 cm by 20 cm by 20 cm. Can Renee cover the chair with 2 m 2 of fabric? Explain. 1. Calculate the SA of all objects 2. subtract 2 faces for each surface where the objects are joined. (We say the faces overlap) ALWAYS check first if you must convert the units!
15 Renee uses 3 pieces of foam to make this chair. Each piece of foam is a right rectangular prism with dimensions 60 cm by 20 cm by 20 cm. Can Renee cover the chair with 2 m 2 of fabric? Explain. 1. Calculate the SA of all objects 2. subtract 2 faces for each surface where the objects are joined. (We say the faces overlap) The surface area of the base of the chair is 0.88 m 2
16 Renee uses 3 pieces of foam to make this chair. Each piece of foam is a right rectangular prism with dimensions 60 cm by 20 cm by 20 cm. Can Renee cover the chair with 2 m 2 of fabric? Explain. 1. Calculate the SA of all objects 2. subtract 2 faces for each surface where the objects are joined. (We say the faces overlap) The surface area of the base of the chair is 0.56 m 2
17 Renee uses 3 pieces of foam to make this chair. Each piece of foam is a right rectangular prism with dimensions 60 cm by 20 cm by 20 cm. Can Renee cover the chair with 2 m 2 of fabric? Explain. 1. Calculate the SA of all objects 2. subtract 2 faces for each surface where the objects are joined. (We say the faces overlap) (0.6 x 0.2) = = 1.2 m 2
18 Renee uses 3 pieces of foam to make this chair. Each piece of foam is a right rectangular prism with dimensions 60 cm by 20 cm by 20 cm. Can Renee cover the chair with 2 m 2 of fabric? Explain. 1. Calculate the SA of all objects 2. subtract 2 faces for each surface where the objects are joined. (We say the faces overlap) (0.6 x 0.2) = = 1.2 m 2
19
20 SA big cube = SA small cube =
21 SA = SA =
22 SA small prism = SA large prism = SA = SA small prism = SA large prism = SA =
23 SA of Warehouse = SA of Loading Dock = TOTAL SA of =
24
25
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