Find the volume and surface area of pyramids and cones

1. Obj. 52 Pyramids and Cones
The student is able to (I can):
• Find the volume and lateral and total surface areas of
pyramids and cones.

2. Volume The volume of a pyramid with base area B
and height h is
1
V Bh
3
=
The volume of a cone is
21 1
V Bh r h
3 3
= = π

3. Examples Find the volume of the following:
1.
2.
2
22 3
B 3 yd
4
= =
= = 31
V ( 3)(3) 3 yd
3
10 mm
10 mm
13 mm
5 mm
12 mm
(Pyth. triple)
21
V (10 )(12)
3
=
3
400 mm=
2 yd
3 yd
2 yd

4. Examples 3.
4.
7 ft.
21 ft.
2 31
V (7 )(21) 343 ft
3
= π = π
25 mi
20 mi
21
V (10 )(25)
3
= π
32500
mi
3
= π

5. Surface Area To find the lateral area of the pyramid, find
the area of each of the faces.
Perimeter of base
slant
height
( )
1
L P
2
=
For the total surface area, add the
area of the base.
S = L + B

6. Likewise, for a cone, the lateral area is
( )
1
L 2 r r
2
= π = π
and the total surface area is
2
S L r= + π

7. Examples Find the lateral and surface area of the
following:
1.
2.
8 in.
20 in.
5 m
5 m
2
8 3
B 6
4
 
=  
 
2
96 3 in=
1
L [(6)(8)](20)
2
=
2
480 in=
2
S 480 96 3 in= +
2
646.3 in≈
5 2 m L (5)(5 2)= π
2
25 2 m= π
2
S 25 2 25 m= π + π
2
189.6 m≈