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Solid Figures 7 th Grade Common Core Georgia Performance Standards: TCV.7.G.6 (3) Solve real-world and mathematical problems involving volume of cubes and right prisms. TCV.7.G.6 (2) Compute the surface area of right rectangular prisms and cubes in real- world and mathematical problems. TCV.6.G.2 Find the volume of a right rectangular prism with fractional edge lengths. Discover and apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. TCV.6.G.4 (1) Represent three-dimensional figures using nets made up of rectangles and triangles. TCV.6.G.4 (2) Use nets to find the surface area of geometric figures in real-world and mathematical problems. Gail Sherman 2013

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Volume CRCT Formula Sheet gives the following formula for the volume of rectangular prisms: V = area of base x h Area of the base is just lw or length x width h is the height, or how tall it is. Huh? What? Pardon Me?

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Volume of a Rectangular Prism What is the shape of the base? rectangle Find area of the base. 3x10 = 30 What is the height? 5 Final Answer? 3x10x5 = 150 units³ 3 10 5

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Your Turn Find area of the base. What is the height? Final Answer? 4 in. 5 in. 9 in. 4 x 5 = 20 9 (l x w) x h= (4x5) x 9 = 180in

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Volume of a Triangular Prism What is the shape of the BIG B base? triangle Find the area of B. (5x10)/2 = 25 What is the height? 4 Final Answer? 4(5x10)/2 = 100 units³ 5 4 10

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Nets Draw a net of a cube. How many faces? 6

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Surface Area of a Cube Let’s name the faces of our cube. Front Back Top Bottom Left Right If each side is 3 inches long, find the surface area.

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Add the areas of the 6 faces! Front is…… 3x3=9 Back is……. 3x3=9 Top is……… 3x3=9 Bottom is… 3x3=9 Left is……… 3x3=9 Right is……. 3x3=9 And the TOTAL is 54 in²

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Rectangular Prism Just a box. Draw a net for this rectangular prism. 4 2 7

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How does your net compare? ☺ It’s ok to be different! ☺ Now find the surface area. 4 2 7

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.. Surface Area of a Rectangular Prism Front = Back = Top = Bottom = Right = Left = Total = 4 2 7

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Rectangular Prism Front = 4x7=28 Back = 4x7=28 Top = 2x7=14 Bottom = 2x7=14 Right = 2x4=8 Left = 2x4=8 Total = 100 units ² 4 2 7

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Nets Draw a net of a triangular prism. How many faces? 4in. 5 in. 2 in.

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Parts of the Triangular Prism Triangle Rectangle 4in. 5 in. 2 in.

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Add the Parts of the Triangular Prism Triangle Rectangle Total = 4in. 5 in. 2 in. ½bh= ½(5x4) =10 lw=5x2 = 10 50 in

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Pyramid Net Draw a net for the square pyramid 5 ft 6 ft

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Use the net to name the parts of the pyramid. Square Triangle 5 ft 6 ft

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Write Formulas & Compute Square Triangle lw = ½ bh= 5x5 = ½ (5x6)= 25 15 85ft

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