© 2010 Pearson Education, Inc. All rights reserved Concepts of Measurement Chapter 13.

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Presentation transcript:

© 2010 Pearson Education, Inc. All rights reserved Concepts of Measurement Chapter 13

Slide Copyright © 2010 Pearson Addison-Wesley. All rights reserved. 13-4Surface Areas  Surface Area of Right Prisms  Surface Area of a Cylinder  Surface Area of a Pyramid  Surface Area of a Cone  Surface Area of a Sphere

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of Right Prisms Lateral area the sum of the areas of the lateral faces Surface area The sum of the lateral surface areas and the area of the bases.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of aCube Cube Surface area = 6e 2

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Right pentagonal prism Surface area = ph + 2B, where p = the perimeter of the base, h is the height of the prism, and B is the area of the base.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Find the surface area of the prism. Example 13-19

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of a Cylinder Right regular prismsRight circular cylinder

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of a Right Circular Cylinder Right circular cylinder Surface area = 2πr 2 + 2πrh

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of a Pyramid

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Right regular pyramid Surface area = where n = the number of faces, is the slant height, and B is the area of the base. Surface Area of a Pyramid The formula for the surface area of a right regular pyramid can be simplified because nb is the perimeter, p, of the base. So,

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Find the surface area of the pyramid. Example 13-20

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Example The Great Pyramid of Cheops is a right square pyramid with a height of 148 m and a square base with perimeter of 940 m. The altitude of each triangular face is 189 m. The basic shape of the Transamerica Building in San Francisco is a right square pyramid that has a height of 260 m and a square base with a perimeter of 140 m. The altitude of each triangular face is 261 m. How do the lateral surface areas of the two structures compare?

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Example (continued) The length of one side of the square base of the Great Pyramid is The lateral surface area of the Great Pyramid is

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Example (continued) The length of one side of the square base of the Transamerica Building is The lateral surface area of the Transamerica Building is The lateral surface area of the Great Pyramid is approximately or 4.9 times as great as that of the Transamerica Building.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of a Cone Cone Surface area = πr 2 + πr where r = radius of the cone and is the slant height.

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of a Cone

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Find the surface area of the cone. Example 13-22

Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide Surface Area of a Sphere Sphere Surface area = 4πr 2