geometry chapter 12 review. lateral area of a prism: l.a. lateral area of a prism: l.a. the lateral...
TRANSCRIPT
GeometryGeometry
Chapter 12 ReviewChapter 12 Review
Lateral Area of a Prism: Lateral Area of a Prism: L.A.L.A.
The lateral area of a right prism equals the perimeter of a base times the height of the prism.
L.A = pH
LA = [2(6) +2(4)] • 8 = 160 square units
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Total Area of a Prism: T.A.Total Area of a Prism: T.A.
The total area of a right prism equals the lateral area plus the areas of both bases.
T.A = L.A. + 2B
LA = 160 + 2(6 • 4) = 160 + 48 = 208 square units
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Volume of a Prism: VVolume of a Prism: V
The volume of a right prism equals the area of a base times the height of the prism.
V = BH
V = (6 • 4) • 8 = 192 cubic units
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The lateral area of a regular pyramid with n lateral faces is n times the area of one lateral face.
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7) Find the lateral area and total area of this regular pyramid.
L.A. = nF
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10
A = ½ b(h)A = 3(10)A = 30
LA = nFLA = 6(30) LA = 180 square units
OR…
The lateral area of a regular pyramid equals half the perimeter of the base times the slant height.
L.A. = ½ pl
LA = ½ plLA = ½ 36(10)
LA = 180 square unitsWe have 6 triangles!
7) Find the lateral area and total area of this regular pyramid.
The total area of a pyramid is its lateral area plus the area of its base.
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T.A. = L.A. + B That makes sense!
A = ½ a(p)
6
30
3
3√3
A = ½ 3√3(36)A = 3√3(18)
A = 54√3
TA = LA + B
TA = 180 + 54√3 sq. units
9. Find the volume of a regular square pyramid with base edge 24 and lateral edge 24.
Draw a square pyramid with the given dimensions.
24
The volume of a pyramid equals one third the area of the base times the height of the pyramid.
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V Bh
V = 1/3 B(h)
V = 1/3 24(24)(h)
V = 8(24)(h)
V = 192(h)12
24
Must be a 30-60-90.
12√312√3
12
122 + x2 = (12√3)2
12√2
V = 192(12√2)V = 2304√2 sq. units
To find volume (V): Start with the area of the base
Multiply it by height
H
r
That’s how much soup is in the can !
A = πr²
V = πr²H
Lateral Area of a Cylinder: Lateral Area of a Cylinder: L.A.L.A.
The lateral area of a cylinder equals the circumference of a base times the height of the cylinder.
L.A = 2πrH
LA = 12π • 8 = 96π square units
L.A = CH
which is
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Total Area of a Cylinder: Total Area of a Cylinder: T.A.T.A.
The total area of a cylinder is the lateral area plus twice the area of a base.
T.A = L.A. + 2B
TA = 96π + 2(π • 6²) = 96π + 2(36π) = 96π + 72π = 168π square units
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T.A. = 2πrH + 2πr²
which is
Lateral Area of a Cone: L.A.Lateral Area of a Cone: L.A.
LA = π • 6 •10 = 60π square units
L.A = πrl 6
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Total Area of a Cone: T.A.Total Area of a Cone: T.A.
The total area of a cone equals the lateral area plus the area of the base.
T.A = L.A. + B
TA = 60π + (π • 6²) = 60π + 36π = 96π square units
T.A. = πrl + πr²
which is
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Volume of a Cone: VVolume of a Cone: V
The volume of a cone equals one third the area of the base times the height of the cone.
V = πr²h
V = 1/3 • π • 6² • 8 = 96π cubic units
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Surface Area FormulaSurface Area Formula24 rSurface Area =
r
Volume FormulaVolume Formula
Volume =34
3r
If the scale factor of two solids is a:b, then
(1) the ratio of corresponding perimeters is a:b
(2) the ratio of base areas, of lateral areas, and of the total area is a²:b²
(3) the ratio of volumes is a³:b³
Scale FactorScale Factor
SCALE FACTOR: 1:2Base circumference: 6π:12π 1:2Lateral areas: 15π:60π 1:4Volumes: 12π:96π 1:8
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HWHW
Chapter 12 WSChapter 12 WS