1. Warm up!

2. today’s agenda Warm up Syllabus Formula sheet Calculator form
Learning!!!
Homework 

3. Unit 1: Circles & volume
Test 1/24

5. CONCEPTS/SKILLS TO MAINTAIN
The introduction to all of the parts of a circle and the relationships of all of those parts to each other will be new to you this semester.
The concepts of Area, Surface Area, and Volume of triangles, special quadrilaterals, and right rectangular prisms were introduced in the 6th Grade Unit 5. This knowledge was built on in the 7th Grade Unit 5 and expanded to include the slicing of right rectangular pyramids. The Volumes of Cones, Cylinders, and Spheres were previously covered in the 8th Grade Unit 3.
The purpose of re-visiting these formulas here in Analytic Geometry is to formalize your understanding of the development of these formulas; to take them from a memorization and use of the formulas to an understanding and application level.

6. Lg 1-1 Volume lg 1-2 the radian lg 1-3 circle theorems
Unit 1: Circles & volume
Lg 1-1 Volume lg 1-2 the radian lg 1-3 circle theorems

7. Learning goal 1-1 question:
How does Cavalieri’s Principle apply to finding the volume of a cylinder, even if it is oblique or not standing straight up?
Essential skills:
Explain Volume Formulas and Use them to solve problems
Extend the study of identifying cross sections of three dimensional shapes to identifying solids of revolution

8. SELECTED TERMS AND SYMBOLS
Cavalieri’s Principle: A method, with formula given below, of finding the volume of any solid for which cross-sections by parallel planes have equal areas. This includes, but is not limited to, cylinders and prisms.
Composite Figures: If a figure is made from two or more geometric figures, then it is called a Composite Figure.
Lateral Area: The sum of the areas of the lateral (vertical) faces of a cylinder, cone, frustum or the like.
Slant Height: The diagonal distance from the apex of a right circular cone or a right regular pyramid to the base.

9. Volume formulas

10. More volume formulas

11. Mixed volume
Complete the “Mixed Volume” worksheet. Whatever you don’t complete in class is your homework 

12. Warm up!

13. Composite solid volume
Composite solids are made up of more than one standard 3D shape.

14. Volume applications
Complete the worksheet on Volume Applications. Finish this for homework 

15. Warm up!

16. This is Sparta! Powered by PRIDE!
Commitment
Cooperation
Integrity
Respect
Responsibility

17. Classroom Behavior Expectations
Students should:
Be on time
Actively participate in class
Follow adult direction
Work collaboratively with peers
Use appropriate language; respond appropriately
Take ownership of actions

18. Hallway Behavior Expectations
Students should:
Walk with purpose
Keep right
One ear bud rule
Be respectful and responsible

19. Important to remember:
Many teachers have their own set of Classroom Behavior Rules or Expectations. These expectations should be followed in addition to any other rules or expectations in your teacher’s class.
From this point on you will be held accountable for following all of these expectations. Consider this your warning 

20. Cavalieri’s principle
Volumes of Cylinders, Cones, Pyramids, and Spheres Task

21. Volume of Cylinders and Cones
What is the difference in volume between cylinders and cones with the same area bases and same height?
How do you find the formula for the volume of a cylinder?
How do you find the formula for the volume of a cone?
Volume Videos:
Volume of a Cone
Volume of a Pyramid
Volume of a Sphere

22. Warm up!
15 minutes

23. Restroom Expectations
Have a pass
Be quick and quiet
Clean up
Be respectful and responsible

24. Lunch Room Expectations
Report and remain
Be quick and quiet.
Clean area
Be respectful and responsible

25. Learning Commons Expectations
Have a pass
Sign in
Work quietly
Be respectful and responsible

26. Volume comparison
The radius of the earth is approximately 3950 miles. The radius of Jupiter is approximately 44,400 miles. Since the radius of Jupiter is more than 11 times that of the earth, which comes closest to the volume of Jupiter ? a) About 11 times that of the earth b) About 121 times that of the earth c) About 600 times that of the earth d. About 1300 times that of the earth
D 5 minutes

27. True or false?
If you double just the width of a rectangular prism then you double its volume.
If you double just the width and height of a rectangular prism then you double its volume.
If you double the width, height, and length of a rectangular prism then you double its volume.
If you double the radius of a circle then you double its circumference.
If you double the radius of a circle then you double its area.
If you double the radius of a sphere then you double its surface area.
T F F T F F 15 minutes

28. Cavalieri’s Principle
The volumes of two objects of the same height are equal if the areas of their corresponding cross sections are equal.

29. Cavalieri’s Principle Examples
These pieces maintain their SAME volume regardless of how they are moved.

30. Cavalieri’s Principle Examples
All heights are the same. Since each cross sections’ area are congruent, all the volumes are equal.

31. Cavalieri’s Principle Examples
The same volume formula applies whether it’s a right prism or an oblique prism. V = Bh

32. Example 1: Which solid has more volume? Use Cavalieri’s Principle.
The area of the cross sections are both 24in2 and have the same height of 20, so the solids have the SAME volume.

33. Example 2: Which solid has more volume? Use Cavalieri’s Principle.
6 cm
10 cm
The area of the cross sections are both 36cm2 and have the same height of 10, so the solids have the SAME volume.

34. QUEEEEEEZ TIME! You have the remainder of class to finish the quiz.
When you have selected your answers, raise your hand and I will check your answers.
If I fold your paper in half, you have earned 100% on the quiz. Congrats! You’re done… tap a nap!
If you have missed any questions, I will tell you the number of questions that you missed. The number I give you does not correspond to the question number.
Example: I do not fold your paper and instead say “One” to you. This means you have missed one question and it is YOUR job to find the incorrect answer and fix it.
Once you feel you have found and corrected your answer, raise your hand again and I will check again.
At this point, it is STILL POSSIBLE to make 100% on the quiz! If I now take and fold your paper, you also have earned 100%! If I tell you another number then you get one more chance to fix your error before I collect the quiz and grade it as is.
GOOD LUCK!