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© 2010 Pearson Education, Inc.All rights reserved
Concepts of Measurement
Chapter 1313
Slide 13.4- 2 Copyright © 2010 Pearson Addison-Wesley. All rights reserved.
13-4 Surface 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 13.4- 3
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 13.4- 4
Surface Area of aCube
Cube
Surface area = 6e2
Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.4- 5
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 13.4- 6
Find the surface area of the prism.
Example 13-19
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Surface Area of a Cylinder
Right regular prisms Right circularcylinder
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Surface Area of a Right Circular Cylinder
Right circular cylinder
Surface area = 2πr2 + 2πrh
Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.4- 9
Surface Area of a Pyramid
Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.4- 10
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 13.4- 11
Find the surface area of the pyramid.
Example 13-20
Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.4- 12
Example 13-21
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 13.4- 13
Example 13-21 (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 13.4- 14
Example 13-21 (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 13.4- 15
Surface Area of a Cone
Cone
Surface area = πr2 + πr where r = radius of the cone and is the slant height.
Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.4- 16
Surface Area of a Cone
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Find the surface area of the cone.
Example 13-22
Copyright © 2010 Pearson Education, Inc. All rights reserved. Slide 13.4- 18
Surface Area of a Sphere
Sphere
Surface area = 4πr2
