

Cavalieri's Principle and Cross Sections
Presentation
•
Mathematics
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9th - 12th Grade
•
Hard
Joseph Anderson
FREE Resource
6 Slides • 5 Questions
1
MAFS.912.G-GMD.1.1 Practice Lesson

2
MAFS.912.G-GMD.1.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments
3
Finding side length of a parallelogram when given a sectioned circle
Circumference=2πr First you need to find the circumference
Area of a circle=2πr2 You will need this formula later
4
Fill in the Blanks
Type answer...
5
Finding side length cont...
Next you need to divide the circumference by 2
Why?
We divide the circumference by 2 because half of the circle makes up each base of the parallelogram.
6
Fill in the Blanks
Type answer...
7
Cavalieri's Principle
If two solids of the same height are such that their corresponding sections at any level have the same areas, then they have the same volume.
8
Multiple Choice
Cavalieri's Principle is most closely hinged on which measurements?
Height and area
Mass and force
Pi and diameter
Radius and pi
9
Cavalieri's Principle
These solids are clearly different, but they have the same height, and the area of the cross sections are equal when the solids are cut, so they have equal volume.
10
Multiple Choice
Would these two solids satisfy Cavalieri's principle?
Yes!
No!
11
Multiple Choice
What are the volumes of cylinder A and B?
110π in3
220π in3
440π in3
550π in3
They do not have the same volume.
MAFS.912.G-GMD.1.1 Practice Lesson

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