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Math Investigation: 4Cylinders, Cones, and Spheres Homework Book

Explore cylinder, cone, and sphere concepts through surface area, volume, and comparison problems. Practice calculating areas and volumes, and understand relationships between shapes.

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Math Investigation: 4Cylinders, Cones, and Spheres Homework Book

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  1. Investigation 4Cylinders, Cones, Spheres

  2. Homework Book Pg 82 A 1,4,5,8,10,15,16,20,25,26,48 B 1,7,9,10,15,17,20,25,26,47,50 IXL AA2 and AA3

  3. Vocab Cylinder Circular bases connected by a rectangle Sphere 3d Circle Cone Circular base, other end comes to a point

  4. Invest 4.1Networking: Surface Area of Cylinders How can you calculate the surface area of a cylinder? Why does that strategy work?

  5. Example Get a net of a cylinder from the front table and work through page 73 problem 4.1

  6. Notes Parts to a Cylinder What is the net Rectangle and 2 circles Surface area C*h+2pir^2

  7. Homework You should be able to have the following problems finished 1

  8. Invest 4.2Wrapping Paper: Volume of Cylinders How can you calculate the volume of a cylinder? How is the procedure similar to calculating the volume of a prism?

  9. Example pg 74 Problem 4.2

  10. Notes Volume of a cylinder Larger the base the greater the volume Area of base times height

  11. Homework You should be able to have the following problems finished A 4 B 7,47

  12. Invest 4.3Comparing Juice Containers: Comparing Surface Area How does the surface area of a cylinder compare to the surface area of a rectangular prism for a given volume?

  13. Example Video Pg 76 problem 4.3

  14. Notes Is a cylinder better, yes more volume What about surface area Square prism is better than a rectangular for volume, what about surface area Cylinder Surface area should be less, but not always skinny and tall would not be productive

  15. Homework You should be able to have the following problems finished A 8,48 B 9

  16. Invest 4.4Filling Cones and Spheres If a sphere and a cone have the same dimensions as a cylinder, how do the volumes compare? What formulas for the volume of a sphere and the volume of a cone can you write using these relationships?

  17. Example Video Volumes comparing

  18. Notes Sphere and cone are less than the cylinder they fit into

  19. Homework You should be able to have the following problems finished A 10,15,16,20 B 10,15,17,20

  20. Invest 4.5Comparing Volumes of Spheres, Cylinders and Cones What are some relationships you can use involving a cone, a sphere, and a cylinder with the same dimensions?

  21. Notes Finding volume of one shape and compare to another

  22. Example Pg 80 and 81 Problem 4.5

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