Surface Area and Volume of Pyramids, Cones, and Spheres 10-5, 10-7,

1
Surface Area and Volume of Pyramids, Cones, and
Spheres 10-5, 10-7, 10-8!!

• I can find the surface areas (lateral and
  total) of pyramids, cones, and spheres.
• I can find the volume of pyramids, cones, and
  spheres.
• I can solve word problems with surface area and
  volume of pyramids, cones, and spheres.

2
Pyramids
l
3
Pyramids
The lateral faces of a regular pyramid can be
arranged to cover half of a rectangle with a
height equal to the slant height of the pyramid.
The width of the rectangle is equal to the base
perimeter of the pyramid.
4
Pyramids
Lateral Surface Area

• LSA

l
Total Surface Area
l
SA LSA B
or
5
Example
Find the lateral area and surface area of the
regular pyramid.
Step 1 Find the base perimeter and apothem.
P 6(10) 60 in.
a
Step 3 Find the surface area.
Step 2 Find the lateral area.
6
Pyramids
Volume

• V

h
7
Example
Find the volume of the regular hexagonal pyramid
with height equal to the apothem of the base
Step 1 Find the area of the base.
2
Step 2 Use the base area and the height to find
the volume.
1296 ft3
8
Cones
9
Cones
Lateral Surface Area
l

• LSA

Total Surface Area
l
SA LSA B
or
10
Example
Find the lateral area and surface area of the
cone.
LSA ?rl
?(8)(17) 136? in2
SA ?rl ?r2
136? ?(8)2 200? in2
11
Cones
Volume

• V

or
h
V
12
Example
Find the volume of a cone.
Step 1 Use the Pythagorean Theorem to find the
height.
162 h2 342
h2 900
h 30
Step 2 Use the radius and height to find the
volume.
2560? cm3
13
Example
Find the volume of a cone with base circumference
25? in. and a height 2 in. more than twice the
radius.
Step 1 Use the circumference to find the radius.
2?r 25?
r 12.5
Step 2 Use the radius to find the height.
h 2(12.5) 2 27 in.
Step 3 Use the radius and height to find the
volume.
1406.25? in3
14
Spheres
15
Spheres
16
Example
Find the surface area and volume of the sphere.
S 4?r2
S 4?(1)2
S 4? m2
17
Example
Find the surface area and volume of the
hemisphere.
S 2?r2 ?r2
2?(11)2 ?(11)2 363? in2
18
Example
Find the surface area and volume of a sphere with
a great circle that has an area of 49? mi2.
A ?r2
49? ?r2
r 7
S 4?r2
4?(7)2 196? mi2
19
Example
20
Example