Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Surface Area of Pyramids and Cones
Vocabulary:
Pyramid

A polyhedron in which the base is a polygon and the lateral faces are triangles with a
common vertex, called the Vertex of the Pyramid.

The intersection of two lateral faces is a Lateral Edge.

The intersection of the base and a lateral face is a Base Edge.
Surface Area of a Pyramid

The sum of the areas of the faces of a polyhedron.
Lateral Surface Area of a Pyramid

The sum of the areas of the lateral faces of a polyhedron.
Height of a Pyramid

The perpendicular distance between the base and the vertex.
Regular Pyramid

Has a regular polygon for a base

The segment joining the vertex and the center of the base is perpendicular to the base.

The lateral faces of a regular pyramid are congruent isosceles triangles.
Slant Height of a Regular Pyramid

The height of a lateral face of the regular pyramid.

A nonregular pyramid does not have a slant height.
Page 1 of 8
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Lateral Surface Area (LSA) and Surface Area (SA) of a Regular Pyramid

For a regular pyramid with base perimeter P, slant height l, and base area B, the
lateral area L and surface area S are:
LSA = Lateral Surface Area
LSA = ½Pl
SA = Total Surface Area
SA = B + ½Pl
Where:
P = Perimeter of the Base
l = Slant Height of the Pyramid
B = Area of the Base
Cone

A solid with a circular base and a Vertex that is not in the same plane as the base.
Height of a Cone

The perpendicular distance between the vertex and the base.
Slant Height of a Right Cone

The distance between the vertex and a point on the edge of the base.

An oblique cone does not have a slant height.
Radius of a Cone

The radius of the base is the Radius of the cone.
Page 2 of 8
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Right Cone

The segment joining the vertex and the center of the base is perpendicular to the base.
Oblique Cone

The segment joining the vertex and the center of the base is not perpendicular to the
base.
Right Cone
Oblique Cone
Lateral Surface Area of a Cone

Consists of all segments that connect the vertex with points on the edge of the base.
Lateral Surface Area (LSA) and Surface Area (SA) of a Right Cone

For a right cone with radius r, slant height l, and base area B, the lateral area L and
surface area S are:
LSA = Lateral Surface Area
LSA =
SA = Total Surface Area
SA =
Where:
r = Radius
l = Slant Height of the Cone
Page 3 of 8
πrl
πr2
+
πrl
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Example 1: Finding Lateral Area and Surface Area
Find the lateral area and the surface area of the regular hexagonal pyramid. Show all work.
P = ________
l = ________
B = ________
LSA = ________
SA = ________
Example 2: Finding Lateral Area and Surface Area
Find the lateral area and the surface area of the regular hexagonal pyramid. Show all work.
P = ________
l = ________
B = ________
LSA = ________
SA = ________
Page 4 of 8
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Example 3: Finding Lateral Area and Surface Area
Find the lateral area and the surface area of the right cone. Show all work.
r = ________
l = ________
LSA = ________
SA = ________
Example 4: Solving a Real-Life Problem
The traffic cone can be approximated by a right cone with a radius of 5.7 inches and a height
of 18 inches. Find the lateral area of the traffic cone. Show all work.
r = ________
l = ________
LSA = ________
Page 5 of 8
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Example 5: Finding the Surface Area of a Composite Solid
Find the lateral area and the surface area of the composite solid. Show all work.
LSASolid = LSACone + LSACylinder
LSACone = ________
LSACylinder = ________
LSASolid = ________
SASolid = LSASolid + BCylinder
LSASolid = ________
BCylinder = ________
SASolid = ________
Page 6 of 8
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Example 6: Changing Dimensions in a Solid
Describe how multiplying all of the linear dimensions
by 3/2 affects the surface area of the right cone.
Show all work.
Original
New
Dimensions
Surface
Area
Multiplying all of the linear dimensions by 3/2 results in a new surface area that is
______________ times the original surface area
Page 7 of 8
Chapter 12 Section 3 - Notes
Name ____________________
Date Due _________________
Period _________
Example 7: Finding the Surface Area of a Composite Solid
Find the lateral area and the surface area of the composite solid. Show all work.
LSASolid = LSAPyramid + LSAPrism
LSAPyramid = ________
LSAPrism = ________
LSASolid = ________
SASolid = LSASolid + BPrism
LSASolid = ________
BPrism = ________
SASolid = ________
Page 8 of 8