Download Document

Name ________________
Geometry Notes
Pyramids & Cones
Pyramids
Our study of pyramids will include only ______________ pyramids.
A regular pyramid is a solid that has only one _______ , and that base must be a ___________
The point at the top is called the _________.
The ___________ of the regular pyramid is directly above the ___________ of the base
and is _______________ to the base.
The distance from the vertex to the base is the ___________ (h).
The faces other than the base are called ____________
_____________.
All lateral faces are ______________. The lateral faces are __________ triangles.
The height of a lateral face is called the _________ _____________ of the pyramid.
(Notice it’s a “slanted height”!)
The slant height is a cursive “ ” on your formula
V
sheet!
Example: In the regular pyramid shown,
2. The vertex is __________
Z
W
1. The base is _________
C
Y
M
X
3. The height is ___________. The slant height is ________.
4. Name a lateral face ____________ How many lateral faces are there? ________
5. Notice that
VCM is a _________ triangle.
6. The slant height will always be __________ than the height of the pyramid.
7. Since there are right triangles in a pyramid, we may use the _________________ theorem.
8. If YX = 20 cm, then CM = ______ cm.
9. If CM = 3 in and CV = 4 in, then VM = _______in.
10. If WY = 12 ft, the perimeter of the base of the pyramid is ____________.
Lateral Area, Surface Area and Volume of Pyramids
Lateral Area of a pyramid
(no base!)
The _________ of all the areas of its lateral faces (triangular lateral faces!).
L. A. formula=
p = perimeter of the base
 = slant height of the pyramid
Example A: Find the lateral area of the pyramid.
V
In the pyramid at right, VC = 12 in and CM = 5 in
Z
W
What is VM?_______
Note that VM is the slant height ()
Sometimes you may have to use Pythagorean Theorem to find the slant height!
C
Y
Looking at the base of the pyramid
M
X
Since CM = 5 in then MZ=_____ XZ=_____ perimeter of square ZXYW=________.
The lateral area is:
Surface area of a pyramid
S. A. formula=
p = perimeter of the base
 = slant height of the pyramid
B = area of base
Example: Find the total surface area of the pyramid above.
() slant height = _______ (p) perimeter = _______
(B) area of base =
Surface Area =
Volume of a pyramid
Volume formula =
B = area of base
h = height of pyramid
Example: Find the volume of the pyramid above.
(B) area of base = _______
(h) height= _______
volume =
Surface Area and Volume of Cones
A cone is a solid with only one ____________ base.

h
The cones that we will study will always be right circular cones.
The ___________ and the circular _________ will always be _______.

Lateral Area of a Cone
Lateral area does _______ include the circular __________.
L.A. formula=
r = radius
 = slant height of the cone
Note: You may have to use Pythagorean Theorem to find the slant height!
Example: Find the lateral area of a cone with radius of 6 cm and height 10 cm.
(r)radius =
() slant height =
lateral area =
Surface area of a cone
S.A. formula=
r = radius
 = slant height of the cone
Example: Find the surface area of cone with r= 6 cm and h= 10 cm.
(r) radius =
() slant height =
surface area =
Volume of a cone:
Volume formula=
r = radius
h = height of cone
Example: Find the volume of a cone with r = 6 cm and h = 10 cm.
(r) radius =
(h) height =
volume =
rr
Examples
1. A pyramid has a square base with sides
of length 220 meters and a height of
145 meters. What is the volume of the
pyramid to the nearest meter?
2. A tepee in the shape of a right cone has a
slant height of 18 feet and a diameter of
20 feet. How much canvas would be
needed to cover the tepee?
(hint: the canvas does NOT go on the ground)
3. The base of a square pyramid is 8 cm
by 8 cm. If the volume of the pyramid
is 128 cm3, what is the height?
4. What is the total capacity (cone and
cylinder) of the storage container
shown below?
8m

6m
12 m
5. The lengths of the sides of the base of a square
pyramid are 4 ft. If the slant height
is 9 feet, what is the surface area of
the pyramid?