Volume and Area
Definitions
• Volume is…The measurement of the space occupied
by a solid region; measured in cubic units
• Lateral Area is… The sum of the areas of the surfaces
of a solid figure NOT including the base(s); measured in
square units.
• Surface or Total area is…The sum of the areas of
the surfaces of a solid figure including the base(s);
measured in square units.
________ Prism
height
width
length
To find volume:
V  lwh
To find lateral area:
LA  ph
To find surface area:
SA  ph  2 B
Example
Find the volume and area.
4 cm
3 cm
8 cm
_________ Pyramid
Height
Width
Length
To find the volume:
1
V  Bh
3
To find the Lateral Area:
1
LA  pl
2
To find the Surface Area:
1
SA  pl  B
2
Example
6 in
3 in
8 in
Find the volume & area.
Sphere
To find the volume:
Radius
4 3
V  r
3
To find the surface area.
SA  4r
2
Example
8m
Find the volume & area.
Cylinder
radius
V  r h
LA  2rh
SA  2rh  2 B
2
height
Example
5 ft
Find the volume & area.
Use 3.14 for π.
7 ft
Cone
height
radius
To find volume:
1 2
V  r h
3
To find the lateral & surface area:
LA  rl
SA  rl  B
Example
Find the volume & area.
6 cm
3 cm
Graded Exit Ticket
The company that produces Sweet Crunch
cereal wants to produce a family-sized box
of its cereal. The regular sized box is a
cube, and each side measures 8 in long.
The company wants to double the length
of the sides of the regular box to create
the family-sized box of cereal. Should the
company just double the price of the
cereal? Why or why not.
Answer
8 in
16 in
Volume 1
V = lwh
V = (8)(8)(8)
V = 512 cubic in
512 1

4096 8
Volume 2
V = lwh
V = (16)(16)(16)
V = 4096 cubic in
The new box of cereal holds 8 times
more cereal. Therefore, the company
should more than double the
price.