warm-up find the surface area of a regular pentagonal pyramid

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

3.

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