1. Chapter 11: Surface Area & Volume
11.2 & 11.3
Surface Area of Prisms, Cylinders, Pyramids, & Cones

2. Definitions prism: bases: lateral faces: altitude: height:
polyhedron with exactly two congruent, parallel faces
bases:
the parallel faces of a prism
lateral faces:
the nonparallel faces of a prism
altitude:
perpendicular segment that joins the planes of the bases
height:
length of an altitude

3. Prisms right prism oblique prism
lateral faces are rectangles and a lateral edge is an altitude
oblique prism
slanted prism

4. Surface Area lateral area of a prism surface area of a prism
sum of the areas of the lateral faces
surface area of a prism
sum of the lateral area and the area of the two bases

5. Example 1
Use a net to find the surface area of the prism:

6. Example 1a
Use a net to find the surface area of the triangular prism:

7. Example 2
What is the surface area of the prism?

8. Example 2a
Use formulas to find the lateral area and surface area of a hexagonal prism with side of length 6 m, and prism height of 12 m.

9. Theorem 11-1
The lateral area of a right prism is the product of the perimeter of the base and the height.
LA = ph
The surface area of a right prism is the sum of the lateral area and the areas of the two bases.
SA = LA + 2B

10. Cylinders two congruent parallel bases that are circles altitude:
perpendicular segment that joins the planes of the bases
height:
length of an altitude

11. Cylinders lateral area: surface area: turns out to be a rectangle
sum of the lateral area and the areas of the two circular bases

12. Theorem 11-2
The lateral area of a right cylinder is the product of the circumference of the base and the height of the cylinder.
LA = 2πrh = πdh
The surface area of a right cylinder is the sum of the lateral area and the areas of the two bases.
SA = LA + 2B = 2πrh + 2πr2

13. Example 3
The radius of the base of a cylinder is 4 in. and its height is 6 in. Find the surface area of the cylinder in terms of π.

14. Example 3a
Find the surface area of a cylinder with height 10 cm and radius 10 cm in terms of π.

15. Definitions pyramid: regular pyramid: slant height:
polyhedron in which one face (base) can be ANY polygon and the other faces (lateral faces) are triangles that meet at a common vertex
regular pyramid:
pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles
slant height:
length of the altitude of a lateral face of the pyramid

16. Pyramid
lateral area
sum of the areas of the congruent lateral faces

17. Theorem 11-3
The lateral area of a regular pyramid is half the product of the perimeter of the base and the slant height.
LA = ½ p l
The surface area of a regular pyramid is the sum of the lateral area and the area of the base.
SA = LA + B

18. Example 1
Find the surface area of the hexagonal pyramid:

19. Example 1a
Find the surface area of a square pyramid with base edges 5 m and slant height 3 m.

20. Cones base is a circle, “pointed” like a pyramid right cone:
altitude is a perpendicular segment from the vertex to the center of the base
height is the length of the altitude
slant height:
distance from the vertex to a point on the edge of the base

21. Theorem 11-4
The lateral area of a right cone is half the product of the circumference of the base and the slant height.
LA = ½·πr·l = πrl
The surface area of a right cone is the sum of the lateral area and the area of the base.
SA = LA + B = πrl + πr2

22. Example 3
Find the surface area of the cone in terms of π, with a radius of 15 cm and slant height of 25 cm.

23. Example 4a
Find the lateral area of a cone with radius 15 in and height 20 in.

24. Homework
p. 611: 1-7, 8, 14
p. 620: even, 18, 20