12.3 Surface Area of
Pyramids and Cones
Geometry
Mr. Peebles
Spring 2013
Geometry Bell Ringer-Whiteboard,
Marker, Towel Please
• Find the surface area of the cylinder in
terms of pi with a radius of 8 in and a
height of 11 in.
• a. 688p in.2
b. 304p in.2
c. 176p in.2
d. 208p in.2
Formula: SA = 2πr2 + 2πrh
Geometry Bell Ringer
• Find the surface area of the cylinder in
terms of pi with a radius of 8 in and a
height of 11 in.
• a. 688p in.2
b. 304p in.2
c. 176p in.2
Answer:
B
d. 208p in.2
Daily Learning Target (DLT)
Monday January 28, 2013
• “I can understand, apply, and remember
to find the surface area of a pyramid
and cone.”
Assignment Due
Pages 611-614 (1, 2, 5, 6, 8, 9, 11, 13, 22,
23, 38-40)
Assignment Due
Pages 611-614 (1, 2, 5, 6, 8, 9, 11, 13, 22,
23, 38-40)
1. 1726 cm2
13. 107 in2
2. 216 ft2
22. C
5. Lateral Area: 120 ft2
23. 47.5 in2
Surface Area: 220 ft2
38. C
6. Lateral Area: 96 in2
39. J
Surface Area: 108 in2
40. D
8. 40π cm2
9. 16.5π cm2
11. 36.8 cm2
Finding the surface area of a
pyramid
• A pyramid is a polyhedron in which the base
is a polygon and the lateral faces are
triangles with a common vertex. The
intersection of two lateral faces is a lateral
edge. The intersection of the base and a
lateral face is a base edge. The altitude or
height of a pyramid is the perpendicular
distance between the base and the vertex.
More on pyramids
• A regular pyramid has a
regular polygon for a
base and its height
meets the base at its
center. The slant height
of a regular pyramid is
the altitude of any
lateral face. A
nonregular pyramid
does not have a slant
height.
Lateral & Surface Area of A
Regular Pyramid
LA = ½ pl
p = Perimeter of Base
l = Slant Height of Pyramid
SA = LA + B
LA = Lateral Area of Pyramid
B = Area of Base
Pyramid Arena
Ex. 1: Finding the Area of a
Lateral Face
• Architecture. The lateral faces of the
Pyramid Arena in Memphis, Tennessee,
are covered with steel panels. Use the
diagram of the arena to find the area of
each lateral face of this regular pyramid.
Ex. 2: Finding the surface area
of a pyramid
• To find the surface area
of the regular pyramid
shown, start by finding
the area of the base.
• Use the formula for the
area of a regular
polygon,
½ (apothem)(perimeter).
A diagram of the base
is shown to the right.
Ex. 2: Finding the surface area
of a pyramid
After substituting, the
area of the base is
½ (3 3 )(6• 6), or
54 3 square meters.
Surface area
• Now you can find the surface area by
using 54 3 for the area of the base, B.
Questions?
Finding the Surface Area of a Cone
• A circular cone, or cone,
has a circular base and a
vertex that is NOT in the
same plane as the base.
The altitude, or height, is the
perpendicular distance
between the vertex and the
base. In a right cone, the
height meets the base at its
center and the slant height
is the distance between the
vertex and a point on the
base edge.
Finding the Surface Area of a Cone
• The lateral surface of a
cone consists of all
segments that connect the
vertex with points on the
base edge. When you cut
along the slant height and
like the cone flat, you get
the net shown at the right.
In the net, the circular base
has an area of r2 and the
lateral surface area is the
sector of a circle.
Theorem
• Surface Area of a Right
Cone
The surface area S of a right
cone is S = r2 + rl,
where r is the radius of the
base and l is the slant
height
Ex. 3: Finding the surface area
of a cone
• To find the surface area
of the right cone shown,
use the formula for the
surface area.
S = r2 + rl
Write formula
S = 42 + (4)(6)
Substitute
Ex. 3: Finding the surface area
of a cone
• To find the surface area
of the right cone shown,
use the formula for the
surface area.
S = r2 + rl
Write formula
S = 42 + (4)(6)
Substitute
S = 16 + 24
Simplify
S = 40
Simplify
The surface area is 40 square inches or about
125.7 square inches.
Questions?
Assignment
Pages 620-623 (1-13 Odds, 23, 27, 28-30,
46-48)
Closure - Whiteboards
Find the surface area of a cone with a radius
of 10 FT and a slant height of 15 FT and
please leave your answer in terms of pi.
Exit Quiz – 5 Points
Find the surface area of the right cylinder.
Leave your answer in terms of pi