Chapter 11: Surface Area & Volume

11.2 & 11.3

Surface Area of Prisms, Cylinders, Pyramids, & Cones

Definitions• prism:

– 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

Prisms• right prism

– lateral faces are rectangles and a lateral edge is an altitude

• oblique prism– slanted prism

Surface Area

• lateral 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

Example 1

• Use a net to find the surface area of the prism:

33

3

44

4

4

3

5

Example 1a

• Use a net to find the surface area of the triangular prism:

12 cm6 cm

5 cm5 cm

Example 2

• What is the surface area of the prism?

6 cm

4 cm3 cm

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.

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

Cylinders

• two congruent parallel bases that are circles

• altitude:– perpendicular segment that joins the planes of the

bases

• height:– length of an altitude

Cylinders

• lateral area:– turns out to be a rectangle

• surface area:– sum of the lateral area and the areas of the two

circular bases

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

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.

Example 3a• Find the surface area of a cylinder with height

10 cm and radius 10 cm in terms of π.

Definitions

• pyramid:– 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

Pyramid

• lateral area– sum of the areas of the congruent lateral faces

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

Example 1• Find the surface area of the hexagonal

pyramid:

6 in

3 3 in

9 in

Example 1a

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

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

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

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.

Example 4a

• Find the lateral area of a cone with radius 15 in and height 20 in.

Homework

• p. 611: 1-7, 8, 14

• p. 620: 2-12 even, 18, 20