Tuesday, April 29, 2008
Geometry (Class 75)
Announcements
Next test is next Friday, April 26. The following test will not be until May 23 due to STAR testing-- that test will cover a lot of material!
Lesson Title
Volume of Sphere
Extended Chords of a Circle
Overview
In today’s class our warm-up focuses on developing the formula for the volume of a sphere. We view a demonstration, analyze what we saw, and draw a conclusion about the relationship between the radius and volume of a sphere. We then confirm our experimental evidence through mathematical analysis. Our lesson for the day continues with our work on segment and arc relationships of circles. In particular we examine the relationship between the lengths of extended chords.
Textbook Sections
§10.5 (Txt. p.629) Segment Lengths in Circles
Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
Cavalieri’s Principle
Key Attitudes
Math is about thinking creatively.
Key Ideas
If two extended chords intersect outside of a circle, then the lengths of the entire extended cords is proportional to the lengths of the sections of the chords exterior to the circle.
The volume of a sphere is equal to four-thirds of the cube of the radius of the shpere.
Key Skills
I can recognize extnded chords and recall the relationship between their lengths.
I can use the relationship between the lengths of the sections of extended chords to solve problems.
I can explain why the relationship between the lengths of extend chords works.
I can recall and use the volume formula for a sphere to solve problems.
I can develop the volume formula of a sphere based on what I know about cones and cylinders.
Turn-In (#74)
Finish Warm-Up (Finding the surface area of an Octagonal Pyramid)
Finish Chapter 10- Lesson 3
Handouts
Chapter 12- Volume of a Sphere
Chapter 10- Lesson 4: Extended Chords of a Circle
Assignment
Finish Chapter 10 Lesson 4
Finish Volume of a Sphere.
Txt. p.632 #10-18, 25
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.
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