Changing the dimensions of an object affects its volume and surface area. If all dimensions are changed by the same factor, the volume changes by that factor cubed and the surface area changes by that factor squared. Examples show how to calculate the new volume or surface area of objects like rectangular prisms, cylinders, hexagonal prisms, and pyramids when their dimensions are changed.

1. Changing Dimensions
The student is able to (I can):
• Calculate changes to the volume of an object if one or
more dimensions change.

2. Just as changing dimensions affects the
perimeter and area of a two-dimensional
object, changing dimensions also affects
the surface area and volume of a three-
dimensional object.
Volume:
If you are changing all dimensions equally,
multiply (or divide) the original volume by
the factor cubed (to the third power).
Surface Area:
If you are changing all dimensions equally,
multiply (or divide) the original surface area
by the factor squared.

3. Examples • A rectangular prism having a volume of
24 ft3 is enlarged by a factor of 5. What
is the new prism’s volume?
• A cylinder having a volume of 72π in3 is
reduced by a factor of 3. What is the
cylinder’s new volume?
( )( ) ( )( )3 3
V 24 5 24 125 3000 ft= = =
3
3
72 72 8
V in
3 27 3
π π π
= = =

4. • A hexagonal prism, which has a total
surface area of 175 cm2, is reduced by a
factor of 5. What is the new surface
area?
• A square-based pyramid has its base
enlarged by a factor of 4 and its height
enlarged by a factor of 3. What happens
to the volume?
2
2
175 175
S 7 cm
5 25
= = =
old
1
V Bh
3
= ( )( )2
new
1
V 4 B 3h
3
1
48 Bh
3
=
 =  
 

5. • A cylinder’s diameter is decreased by a
factor of 5 and its height is increased by
a factor of 3. What happens to the
lateral surface area?
oldL dh= π
( )
( )
new
d
L 3h
5
3
dh
5
 = π 
 
= π