obj. 44 volume
TRANSCRIPT
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Volume
The student is able to (I can):
Calculate the volume of prisms, cylinders, pyramids, and cones
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right prism
oblique prism
altitude
A prism whose faces are all rectangles.
A prism whose faces are not rectangles.
A perpendicular segment joining the planes of the bases (the height).
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Volume Lets consider a deck of cards. If a deck is stacked neatly, it resembles a right rectangular prism. The volume of the prism is
V = Bh,
where B is the area of one card, and h is the height of the deck.
If we shift the deck so that it becomes an oblique prism, does it have the same number of cards?
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For any prism, whether right or oblique, the volume is
V = Bh
where h is the altitude, not the length of the lateral edge.
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Likewise, for cylinders, it doesnt matter whether the cylinder is right or oblique, the volume is
V = Bh = pir2h
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Examples Find the volume of each figure:
1.
2.
10 ft.
8 ft.
3 m
19 m
( )2 2B 3 9 m= pi = pi3V (9 )(19) 171 m= pi = pi
( )1 5B 50 172.052 tan36
= =
V = (172)(8) = 1376 ft3
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The volume of a pyramid with base area B and height h is
1V Bh
3=
The volume of a cone is
21 1V Bh r h3 3
= = pi
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Examples Find the volume of the following:
1.
2.
222 3B 3 yd
4= =
= =31V ( 3)(3) 3 yd
3
10 mm10 mm
13 mm
5 mm
12 mm(Pyth. triple)
21V (10 )(12)3
=
3400 mm=
2 yd
3 yd
2 yd
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Examples 3.
4.
7 ft.
21 ft.2 31V (7 )(21) 343 ft
3= pi = pi
25 mi
20 mi
21V (10 )(25)3
= pi
32500 mi3
= pi