8 3 Area Volume and Surface Area Copyright

Area Formulas Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra

Helpful Hint Area is always measured in square units. When finding the area of

Radius r Given a circle of radius, r, the circumference is C = 2π

Area of a Circle Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Area of a Circle 64 equal sectors 128 equal sectors πr πr r r

Plane Figures Plane Figure Drawing Perimeter/ Circumference Area P = a + b +

Volume measures the number of cubic units that fill the space of a solid.

Surface Area A polyhedron is a solid formed by the intersection of a finite

Volume The volume of a solid is the number of cubic units in the

Rectangular Solid height width length Volume = length ∙ width ∙ height V =

Cube side Volume = side ∙ side V = s 3 SA = 6

Sphere radius Volume = Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

Circular Cylinder height radius Volume = V = πr 2 h SA = 2πrh

Cone height radius Volume = Copyright © 2011 Pearson Education, Inc. Publishing as Prentice

Square-Based Pyramid height side B = area of base, p = perimeter, l =

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Helpful Hint 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. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 4

Area of a Circle 64 equal sectors 128 equal sectors πr πr r r πr πr 2 n equal sectors Notice the rectangular shape. A = lw πr r A = (πr)r πr A = πr 2 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 7

Plane Figures Plane Figure Drawing Perimeter/ Circumference Area P = a + b + c Triangle Parallelogram P = a + b + c + d Rectangle P = 2 l + 2 w Square P = 4 s A = bh A = lw A = s 2 P = a + b + c + d Trapezoid C = π d or 2π r Circle A = πr 2 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 8

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. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 9

Surface Area A polyhedron is a solid formed by the intersection of a finite number of planes. 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. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Martin-Gay, Prealgebra & Introductory Algebra, 3 ed 10

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

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

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