area, volume, and surface area
DESCRIPTION
Section 9.3. Area, Volume, and Surface Area. Area of a Rectangle. Area is measured in square units. A square unit is a square one unit on each side. For example, start with a rectangle with length ( l ) 3 units and width ( w ) 2 units. A = l • w A = 3 • 2 units 2 A = 6 units 2. 2. - PowerPoint PPT PresentationTRANSCRIPT
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Area, Volume, and Surface Area, Volume, and Surface AreaArea
Section 9.3
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Area of a RectangleArea of a Rectangle
AreaArea is measured in square units. A is measured in square units. A square unit is a square one unit on each square unit is a square one unit on each side.side.
2
3
For example, start with a rectangle with For example, start with a rectangle with length (length (ll) ) 3 units and width ( units and width (ww) ) 2 units. units.
A l • w
A 3 • 2 units2
A 6 units22
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3 • 2 6 A bh
The diagonal of
a parallelogram
forms 2
congruent triangles.
3
2
2
3
3 • 2 6
A lw
RectangleRectangle
3
2
TriangleTriangle
Area Area FormulasFormulas
1A bh2
(3 • 2) 3 1
2
ParallelogramParallelogram
3
2
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area side • side
A s • s s
2
More Area More Area FormulasFormulas
B
B
bb+
h
h
SquareSquare
side
side
TrapezoidTrapezoid
1( )
2B b
1( )
2A B b
4Martin-Gay, Prealgebra, 5ed
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AreaArea is always measured in square units. is always measured in square units.
When finding the area of figures, check to When finding the area of figures, check to make sure that all measurements are the make sure that all measurements are the same units before calculations are made.same units before calculations are made.
Helpful HintHelpful Hint
5Martin-Gay, Prealgebra, 5ed
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r
Given a circle of radius, Given a circle of radius, r,, the the circumference iscircumference is C 2 r.
6Martin-Gay, Prealgebra, 5ed
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Area of a CircleArea of a Circle
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Notice the rectangular shape.
A lw
A (r)r
A r
2
equal sectorsn
2
r
r
r
64 equal sectors
r
r
r
128 equal sectors
r
r
r
Area of a CircleArea of a Circle
8Martin-Gay, Prealgebra, 5ed
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P a b c
P a b c d
P 2l 2w
P 4s
P a b c d
Plane Figure DrawingPerimeter/
Circumference Area
Triangle
Parallelogram
Rectangle
Square
Trapezoid
Circle C d or 2 r
A bh
A lw
A s2
A r 2
1( )
2A B b h
1
2A bh
9Martin-Gay, Prealgebra, 5ed
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VolumeVolume measures the number of cubic measures the number of cubic units that fill the space of a solid. The units that fill the space of a solid. The volume of a box or can is the amount of volume of a box or can is the amount of space inside.space inside.
Volume can be used to describe the Volume can be used to describe the amount of juice in a pitcher or the amount amount of juice in a pitcher or the amount of concrete needed to pour a foundation for of concrete needed to pour a foundation for a house.a house.
VolumeVolume
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A A polyhedron polyhedron is a solid formed by the is a solid formed by the intersection of a finite number of planes.intersection of a finite number of planes.
Surface AreaSurface Area
11
The The surface area surface area of a polyhedron is the of a polyhedron is the sum of the areas of the faces of the sum of the areas of the faces of the polyhedron.polyhedron.
Surface area is measured in square units.Surface area is measured in square units.
Martin-Gay, Prealgebra, 5ed
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The volume of a solid is the number of The volume of a solid is the number of cubic unitscubic units in the solid. in the solid.
1 centimeter1 centimeter
1 centimeter
1 inch1 inch
1 inch
1 cubic centimeter 1 cubic inch
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Rectangular SolidRectangular Solid
length
widthheight
Volume length width height
V = lwh
SA = 2lh + 2wh + 2lw
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CubeCube
sideside
side
Volume = side side side
V = s3
SA = 6s3
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SphereSphere
3( adi4
r3
us) Volume
radius
34
3V r
15
24SA r
Martin-Gay, Prealgebra, 5ed
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Circular CylinderCircular Cylinder
Volume
V r2h
radius
height
2( adius) ( ht)r heig
16
SA 2 r h + 2r2
Martin-Gay, Prealgebra, 5ed
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ConeCone
Volume
radius
height
21
3V r h
2( adius) (1
r hei3
ght)
17 2 2 2S hA r rr
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Square-Based PyramidSquare-Based Pyramid
Volume
height
side13
2 ( )side height
V = 13
s2h
18
1
2SA B pl
B = area of base, p = perimeter, l = slant height
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Helpful HintHelpful Hint
Volume is always measured in Volume is always measured in cubic unitscubic units..
19
Surface area is always measured in Surface area is always measured in square square unitsunits..
Martin-Gay, Prealgebra, 5ed