Transcript Document

Surface Area of Pyramids and Cones
Section 12.3
Goal –
to find the surface area of a pyramid
and the surface area of a cone
Pyramids & Cones
Pyramid – a polyhedron where the base is a polygon and the lateral
faces are triangles with a common vertex.
Cone– a solid with a circular base and a vertex that is not in the same
plane as the base.
lateral edge
vertex
slant height "l "
height "h " or altitude
circular base
base (regular polygon)
radius
Pyramids are classified by the shapes of their
bases
Surface Area verses Lateral Area
of a Pyramid
The lateral area of a pyramid:
LA =
1
2
Pl
P = Perimeter of the base
l = slant height
The surface area of a pyramid:
SA =
1
2
Pl  B
B = Area of the base
Example
Find the LA and SA of the square pyramid.
slant height "l "
12 cm
12 cm
10 cm
10 cm
5 cm
Surface Area verses Lateral Area
of a Cone
The lateral area of a cone:
LA =  rl
r = radius of the base
l = slant height
The surface area of a cone:
2

rl


r
SA =
Example
Find the LA and SA of the cone if the slant height "l" = 8 inches,
and r = 5 inches.
slant height "l "
8
5
Students
Find the LA and SA of the cone if the height "h" = 16 inches,
and the diameter = 24 inches.
Students
Find the LA and SA of the pyramid.
h  15 cm
12 cm
12 cm
Students
regular pyramid
Find the lateral and surface area.
l  15 cm
A  100 cm2