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Solid Figures

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.

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Solid Figures

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  1. Solid Figures 7th 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

  2. What? Huh? Pardon Me? 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.

  3. 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 5 10

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

  5. 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

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

  7. 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.

  8. 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

  9. 2 4 7 Rectangular Prism • Just a box. • Draw a net for this rectangular prism.

  10. 2 4 7 How does your net compare? ☺It’s ok to be different!☺ Now find the surface area.

  11. 2 4 7 . Surface Area of a Rectangular Prism . • Front = • Back = • Top = • Bottom = • Right = • Left = • Total =

  12. 2 4 7 Rectangular Prism • Front = 4x7=28 • Back = 4x7=28 • Top = 2x7=14 • Bottom = 2x7=14 • Right = 2x4=8 • Left = 2x4=8 • Total = 100 units ²

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

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

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

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

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

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

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