oh no, here we go again. theorem 11-5: cavalieri’s principle if two space figures have the same...
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Oh no, here we go again.
Theorem 11-5: Cavalieri’s Principle
If two space figures have the same height and the same cross-sectional area at every level, then they have the same volume.
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Example:
32
32 2
6
A=lw
A=32A=6 units2
A=lw
A=32A=6 units2
Since they all have the same area, then they have the same volume.
A=.5b h
A=.5 62A=6 units2
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Theorem 11-6: Volume of a Prism
The volume of a prism is the product of the area of the base and the height of the prism.
V=Bareah
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Example:
32
32 2
6
A=lw
A=32A=6 units2
A=lw
A=32A=6 units2
A=.5bh
A=.562A=6 units2
10 10 10
V=Bh
V=610
V=60 units3
V=610
V=60 units3
V=610
V=60 units3
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Theorem 11-7: Volume of a Cylinder
The volume of a cylinder is the product of the area of the base and the height of the cylinder
V=Bareah
V=r2h
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Example:
8 cm
3 cmV=r2h
V=(3cm)2(8cm)V=(72cm3)
V=804.2cm3
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Volume of
Composite Space Figure
Find the volume of each figure and then add the volumes together.
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Example:
12 in.4 in.
17 in.
12 in.4 in.
11 in.
4 in.6 in.
V = r2h( )/2V = (·62·4)/2V = 226in3
V = lwh
V = 12411
V = 528in3
V=226in3+528in3
V=754in3
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