warm-up find the surface area of a regular pentagonal pyramid
TRANSCRIPT
Warm-up
• Find the surface area of a regular pentagonal pyramid
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tan54 =a5
5tan54 =a6.88 ≈a
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B=12aP
B=12(6.88)(50)
≈172.05
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S=B+12Pl
S=172+12(50)(13)
S≈497.05square units
Volume of a Solid
• The number of cubic units contained in the interior of a solid.
Volumeof prism, cylinder = area of base x height
V = Bh V = BhorV = ∏r2 h
Find the volume to the nearest tenth.
• V=Bh
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V = 6(13)(3)V = 234 in3
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B=142 3
4
B=196 3
4B=49 3
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V =49 3 • 12V =588 3V =1018.4cm3
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V =π32 • 4V =36πV =113.1cm3
Volume Congruence Postulate
• The volume of a solid is the sum of the volumes of all its non-overlapping parts.
Volume Addition Postulate
• If two polyhedra are congruent, then they have the same volume.
Cavalieri’s Principle
• If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
Use the Cavalieri’s Principle to find the volume of the oblique prism or cylinder.
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V =πr2hV =π22 • 5V =20π in3
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V =BhV =4 • 6 • 3V =72mm3