 # Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 8.3 Area, Volume, and Surface Area.

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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. Dividing the circle into 4 equal sectors, half the circumference, πr, is blue and the other half is red. r πrπr πrπr 32 equal sectors r πrπr πrπr 16 equal sectors πrπr πrπr r 8 equal sectors r πrπr πrπr 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 2 n equal sectors πrπr πrπr r 64 equal sectors πrπr πrπr r 128 equal sectors πrπr r πrπr 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  dP  a  b  c  d P  2l  2w P  4s P  a  b  c  dP  a  b  c  d Plane FigureDrawing Perimeter/ Circumference Area Triangle Parallelogram Rectangle Square Trapezoid Circle C  π d or 2π r A  bh A  lw A  s2A  s2 A  πr 2A  πr 2 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 10 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.

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The volume of a solid is the number of cubic units in the solid. 1 centimeter 1 inch 1 cubic centimeter 1 cubic inch Volume

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rectangular Solid length width height Volume = length ∙ width ∙ height V = lwh SA = 2lh + 2wh + 2lw

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Cube side Volume = side ∙ side ∙ side V = s 3 SA = 6s 3

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 14 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Sphere Volume  radius

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Circular Cylinder Volume  V  πr 2 h radius height SA  2πrh + 2πr 2

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Cone Volume  radius height

Martin-Gay, Prealgebra & Introductory Algebra, 3ed 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Square-Based Pyramid height side B = area of base, p = perimeter, l = slant height