Surface Area & Volume

OBJECTIVES• Slices of 3-dimensional figures• Nets of 3-D solids• Lateral areas, surface areas,volumes of solids• Properties of congruent & similar solids

3-dimensional figuresYou will use different math websites for

visualizations of 3-D figures. • Take time to use these sites to help explain the

material.• Refer back to them for formulas, detailed

diagrams, and rotations• If the links are blocked by your firewall, copy the

URL & paste it in the address on your homepage• Bookmark them or add to ‘favorites’ while you’re

in this course.

Websites for 3-dimensional geometryhttp://www.mathsisfun.com/platonic_solids.html

http://www.mathsisfun.com/geometry/index.html

http://mathforum.org/alejandre/workshops/polyhedra.html

http://mathforum.org/library/drmath/sets/high_geom.html

http://www.houseof3d.com/pete/applets/graph/index.html

Nets & surface areas• Nets are ‘flattened’ 3-D figures– it’s the pattern to

make the shape by folding.• Refer to the text for vocabulary and diagrams as

well as the websites• Add areas of all non-overlapping sections of the net

for each polygon for surface area of figure.

http://www.mathsisfun.com/platonic_solids.html

Surface area of prisms & cylinders

• Refer to the websites and your text for diagrams and vocabulary: bases, lateral edges, altitude, prism & cylinder

• Lateral area is the surface area minus the bases• Surface area includes both bases

L.A. = Ph = 2 π r h

S.A. = Ph+2π r2 = 2 π r h + 2π r2

L.A. = P h

S.A. = P h + 2B

Right cylinder Regular prism

Surface areas of pyramids & cones

• Refer to the websites and your text for diagrams and vocabulary: base, vertex, lateral faces & edges, altitude, and slant height.

• Refer to these resources for formulas

http://www.mathsisfun.com/geometry/pyramids.html

Volume of prisms & cylinders

• Right prisms: Volume = B • h, where B = area of base & h = height

• Right cylinder:Volume = B • h = π r 2 h

Volume of pyramids & cones• Volume of Right pyramids:

V =

• Volume of right cone:

V =

Cavalarieri’s Principle: 2 solids of same height & same cross-sectional area have the same volume.

1B h, where B = area of base

3

21 1B h = h r

3 3

Surface area & volume of spheres

• Refer to text for vocabulary

• Surface Area = 4 π r 2

• Volume = 34

r3

Congruent & similar solids2 solids are congruent if:

2 solids are similar:

if ratio of 2 solids are a : b, then

surface area ratio – a 2 : b2

volume ratio – a 3 : b3

corr 's & corr edges

areas of corr faces & volumes