12 2 surface areas of prisms and cylinders lesson
11
12.2 Surface Area of Prisms & Cylinders p. 728 NCSCOS: 1.02, 2.03, 2.04
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Transcript of 12 2 surface areas of prisms and cylinders lesson
12.2 Surface Area of Prisms & Cylinders
p. 728
NCSCOS: 1.02, 2.03, 2.04
DefinitionsDefinitions• Prism – polyhedron with 2 faces (called
bases) that lie in planes.– Named by the shape of the bases.
• Lateral Faces – the faces that are NOT bases (all are ’ogram shaped)
• Lateral Edges – edges of the lateral faces that are NOT edges of the bases as well.
• Height (altitude) - distance between the bases.
• Right Prism – lateral edges are to bases.• Oblique Prism – lateral edges are NOT
to the bases. (looks slanted)
Right Oblique
Triangular PrismsTriangular Prisms
Bases (2 Δs)
Lateral edges (3)
Lateral faces (3 ll’ograms)
height
3-D Areas
• Lateral Area (LA) – the sum of the areas of the lateral faces only.– Does not include the area of the bases.
• Surface Area (S) – the sum of the areas of ALL the faces.– Lateral area + area of the bases
Net• Defn. – a 2-dimensional
representation of a solid.
• Just think “unfold” the figure and lie it flat.
• Ex:
To find surface or lateral areas, you could find the areas of each individual
face and then add them all together; OR you could use formulas!
Thm 12.2 – SA of a rt. Prism
S = 2B + Ph
B = area of base, P = perimeter of base, h = height of prism
What about Lateral Area?
* remember: LA is everything BUT the bases!
So, LA = Ph
Ex: Find the lateral & surface areas of the triangular prism.
LA = Ph
P = 6*3 = 18
LA = 18*10
LA = 180 in2
S = 2B + Ph
S = 2(15.59) + 180
S = 31.18 + 180
S = 211.18 in2
6 in
.
10 in.
B= s2 √34
=36√34
=9√3 ¿ 15 .59
60o
Cylinder• Defn. – solid with , circular bases.
• Can be right or oblique.
• Lateral Area – the area of the curved surface.
What does the curved surface look like if lied out flat?
Think of the label of a soup can!
It’s a rectangle! (area of rectangle = bh)
• Surface Area – lateral area + area of bases.
h
h
Thm 12.3: SA of a rt. cylinderLet’s look at lateral area 1st!
LA = Ch
or
LA = 2rh
So, S = 2B + Ch
or
S = 2r2 + 2rh
Ex: Find the lateral & surface areas of the cylinder.
LA = 2rh
LA = 2(4)(8)
LA = 64 m2
Or 201.06 m2
S = 2r2 + 2rh
S = 2(42) + 64S = 32 + 64
S = 96 m2
Or 301.59 m28
m.
4 m.
You can find SA of cylinder records used on photographs
during 1800s.
http://history.sandiego.edu/GEN/recording/notes.html
