Smc3 direct - lesson #76 - volume of prisms and cylinders
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Saxon Math: Course 3Lesson #76 :Volume of Prisms and Cylinders
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“Do Now”• Read Saxon Math Book pages 508 - 510• Deﬁne: (Write the bolded deﬁnitions in your own words) 1. Volume 2. Base of a Prism 3. Height of a Prism2. Answer the following Questions 1. How do you ﬁnd the volume of a prism? 2. Why is it helpful to sketch/draw the base of a prism when ﬁnding its volume?
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Class Expectations• Taking Notes • Write Everything that is in RED• Clipboard Checks• Sentence Detention
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Lesson 76: Volume of Prisms and Cylinders• Lesson Objectives: 1. I will be able to use the formula V = Bh to calculate the volumes of prisms and cylinders 2. I will be able to compare the volumes of similar solids
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Lesson Agenda Parts of a Prism --- 8 minutes Volume of Prisms --- 6 minutesVolume of Cylinders --- 4 minutes
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Parts of a Prism 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! • the parallel surfaces at opposite ends of a ﬁgure 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! • the parallel surfaces at opposite ends of a ﬁgure • the shape that looks stretched 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! • the parallel surfaces at opposite ends of a ﬁgure • the shape that looks stretched • Sketch the base of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! • the parallel surfaces at opposite ends of a ﬁgure • the shape that looks stretched • Sketch the base of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! • the parallel surfaces at opposite ends of a ﬁgure • the shape that looks stretched • Sketch the base of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Base of a Prism - Your Deﬁnitions! • the parallel surfaces at opposite ends of a ﬁgure • the shape that looks stretched • Sketch the base of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism• Bases are highlighted in RED 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Height of a Prism - Your Deﬁnitions! • perpendicular distance between the bases • how far the base is “stretched” • Determine the height of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Height of a Prism - Your Deﬁnitions! • perpendicular distance between the bases • how far the base is “stretched” • Determine the height of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Height of a Prism - Your Deﬁnitions! • perpendicular distance between the bases • how far the base is “stretched” • Determine the height of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Height of a Prism - Your Deﬁnitions! • perpendicular distance between the bases • how far the base is “stretched” • Determine the height of the following 3-D shapes 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Parts of a Prism • Height is in RED 3 ft 3 ft 7 in. 5 in. 5 ft5 in. 12 in. 16 ft 3 in. 10 ft 4 in. 20 ft
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Group Practice• Sketch the base and determine the height for each of the following 3-D ﬁgures 13 cm. 3 in. 5 cm.3 in. 15 cm. 2 in. 7 in. 4 in. 12 cm. 2.5 ft 2.5 ft 0.25 m. 3.54 ft 1.74 m 8 ft 3 ft 10.5 ft
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Group Practice• Sketch the base and determine the height for each of the following 3-D ﬁgures 13 cm. 3 in. 5 cm.3 in. 15 cm. 2 in. 7 in. 4 in. 12 cm. 2.5 ft 2.5 ft 0.25 m. 3.54 ft 1.74 m 8 ft 3 ft 10.5 ft
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Group Practice (Answers) 3 in. 13 cm. 5 cm. 2 in. 12 cm. 4 in. h = 7 in. h = 15 cm. 2.5 ft 2.5 ft 0.25 m. 8 ft 3 ft 10.5 fth = 1.74 m. h = 3.54 ft.
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Group Practice (Answers) 3 in. 13 cm. 5 cm. 2 in. 12 cm. 4 in. h = 7 in. h = 15 cm. 2.5 ft 2.5 ft 0.25 m. 8 ft 3 ft 10.5 fth = 1.74 m. h = 3.54 ft.
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Volume of a Prism• Step #1: Sketch Base• Step #2: Determine height• Step #3: Find area of Base• Step #4: Multiply Base Area and height Find the Volume of the following shape 7 in. 7 in. 5 in. 9 in. 4 in.
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Volume of a Prism• Step #1: Sketch Base• Step #2: Determine height• Step #3: Find area of Base• Step #4: Multiply Base Area and height Find the Volume of the following shape 7 in. 7 in. 5 in. 9 in. 4 in.
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Volume of a Cylinder (Example)• Find the volume of the following cylinder 5 cm. 6.05 cm.
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Volume Group Practice• Saxon Math Book p. 511 • a-d• When you are done, raise your hand, and I will hand out the worksheet
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Group Practice Answers• a)105 ft 3• b) 940 ft 3• c) 4000 ft 3• d) 240 cm 3
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Worksheet• Try to do every problem by yourself• If in doubt, ask your partner• If you and your partner are in doubt, raise your hand
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Study Check• Investigation #5: Graphing Transformations
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