1. 14 Chapter Area, Pythagorean Theorem, and Volume
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

2. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
14-4 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 © 2013, 2010, and 2007, Pearson Education, Inc.

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 © 2013, 2010, and 2007, Pearson Education, Inc.

4. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Surface Area of aCube
Cube
Surface area = 6e2
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

5. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
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 © 2013, 2010, and 2007, Pearson Education, Inc.

6. Example 14-14a Find the surface area of the prism.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

7. Surface Area of a Cylinder
Right regular prisms
Right circular cylinder
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

8. Surface Area of a Right Circular Cylinder
Surface area = 2πr2 + 2πrh
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

9. Surface Area of a Pyramid
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

10. Surface Area of a Pyramid
Right regular pyramid
Surface area = where n = the number
of faces,  is the slant height, and B is the area of the base.
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 © 2013, 2010, and 2007, Pearson Education, Inc.

11. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example 14-15
Find the surface area of the pyramid.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

12. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example 14-16
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 © 2013, 2010, and 2007, Pearson Education, Inc.

13. 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 © 2013, 2010, and 2007, Pearson Education, Inc.

14. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
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 © 2013, 2010, and 2007, Pearson Education, Inc.

15. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Surface Area of a Cone
Cone
Surface area = πr2 + πr where r = radius of the cone and  is the slant height.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

16. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Surface Area of a Cone
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

17. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example 14-17
Find the surface area of the cone.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

18. Surface Area of a Sphere
Surface area = 4πr2
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.