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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
8.3
Area, Volume, and Surface Area
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Area Formulas
Continued.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Area Formulas
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Area is always measured in square units.
When finding the area of figures, check to make sure that all measurements are in the same units before calculations are made.
Helpful Hint
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
r
Given a circle of radius, r, the circumference is C = 2π r.
Radius
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Area of a Circle
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Notice the rectangular shape.
A lw
A (πr)r
A πr 2
2n equal sectors
πr
πr
r
64 equal sectors
πr
πr
r
128 equal sectors
πr
r
πr
Area of a Circle
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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 π d or 2π r
A bh
A lw
A s2
A πr 2
=1
( )2
A B + b h
=1
2A bh
Plane Figures
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Volume measures the number of cubic units that fill the space of a solid. The volume of a box or can is the amount of space inside.
Volume can be used to describe the amount of juice in a pitcher or the amount of concrete needed to pour a foundation for a house.
Volume
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
A polyhedron is a solid formed by the intersection of a finite number of planes.
Surface Area
The surface area of a polyhedron is the sum of the areas of the faces of the polyhedron.
Surface area is measured in square units.Surface area is measured in square units.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
The volume of a solid is the number of cubic units in the solid.
1 centimeter1 centimeter
1 centimeter
1 inch1 inch
1 inch
1 cubic centimeter 1 cubic inch
Volume
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Rectangular Solid
length
widthheight
Volume = length ∙ width ∙ height V = lwh
SA = 2lh + 2wh + 2lw
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Cube
sideside
side
Volume = side ∙ side ∙ side
V = s3
SA = 6s3
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Sphere
V =
4
3 r3
SA = 4 r2
Volume
radius
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1515
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Circular Cylinder
Volume
V πr2h
radius
height
SA 2πrh + 2πr2
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1616
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Cone
V =
1
3 r2h
Volume
radius
height
SA = r r2 + h2 + r2
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1717
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Square-Based Pyramid
height
side
B = area of base, p = perimeter, l = slant height
Volume = side) height 21(
321
3V s h
1
2SA B pl
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