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Solid Figures

Solid Figures. Gail Sherman 2010. 6 th Grade Georgia Performance Standards: M6M3 Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids, and cones).

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Solid Figures

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  1. Solid Figures Gail Sherman 2010 6th Grade Georgia Performance Standards: M6M3 Students will determine the volume of fundamental solid figures (right rectangular prisms, cylinders, pyramids, and cones). M6M4Students will determine the surface area of solid figures (right rectangular prisms and cylinders).

  2. What? Huh? Pardon Me? Volume • CRCT Formula Sheet gives the following formula for the volume of all right solid figures: V = Bh • Big B stands for the area of the base. • Small b stands for the base of a plane figure, like a triangle. • Very confusing.

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

  4. Volume of a Cylinder • What is the shape of B? • circle • Find the area of B. • πx 4² = 16 • What is the height? • 9 • Final answer? • πx 4² x 9 = 144π 4 9

  5. Volume of a Cone • This cone & cylinder have the same size bases and they are the same height. Do they both hold the same amount of water? • Which one holds more? • How much more? • Let’s experiment…

  6. Volume of a Cone • You know that cylinder volume = Bh. • You know a cone is 1/3 the volume of a cylinder. • So…Volume of a cone is:

  7. Volume of a Cone • Find the volume of the cone. • Radius is 5. • Height is 4

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

  9. 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.

  10. 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

  11. 2 4 7 Rectangular Prism • Just a box. • Draw a net for this rectangular prism.

  12. 2 4 7 How does your net compare? ☺It’s ok to be different!☺ Now find the surface area.

  13. . Surface Area of a Rectangular Prism . • Front = • Back = • Top = • Bottom = • Right = • Left = • Total =

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

  15. Do You See Any Shortcuts? • S.A. =2(lw+lh+wh) • S.A. = 2wl+2hl+2wh

  16. Cylinders • Draw a net of a soup can.

  17. Net of a Cylinder ☺It’s ok to be different!☺

  18. Find Surface area • If the soup can is 10 inches tall and has a radius of 3 inches. 3 10

  19. Hints… • Look back at your net • 2 circles • What’s that formula again? • 1 rectangle • I know the height • What is the width? • Add the parts together

  20. Voila! • πr² gives me area of a circle. • 3.14 x 3 x 3 = • I have 2 of them, so I’ll multiply that by 2 = • 2πr gives me circumference (width of rectangle) • 2 x 3.14 x 3 x 10 =188.4 Top = 28.26 Bottom = 28.26 Rectangle = 188.4 TOTAL = 244.92 in²

  21. Answering With Pi • Sometimes there is no need to compute pi, because they want the answer to be precise and contain pi. • In that case: • πr² = π x 3² = 9π • 2πr = 2 x π x 3 x 10 = 60π • 9π + 9π + 60π = 78π

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