6th Grade Math Textbook, Fundamentals

 &KDSWHU

11-11

Changing Dimensions of

Three-Dimensional Figures

Objective To understand how change of scale relates to change in dimensions •To understand

how changes in scale and dimension relate to changes in volume and surface area

A sculpture is planned to be put in front of a civic center.
The shape of the sculpture will be a rectangular prism
with length 6 feet, width 3 feet, and height 9 feet. The

sculptor built a model with a scale factor of. How

does the surface area of the scale model compare to the
surface area of the actual sculpture?

To compare surface areas, first find the dimensions of the model.
Then compute the surface area of each and compare.

The scale factor for comparing a dimension of the

model to the corresponding dimension of the sculpture

is. So multiply each dimension of the sculpture by

to find the corresponding dimension of the model.

model length  • 6 feet 4 feet

model width  • 3 feet 2 feet

model height  • 9 6 feet

Find the surface areas of the sculpture and the model.

Smodel  2 w 2 h 2 wh Ssculpture 2 w 2 h 2 wh

2(8) ft 2(24) ft 2(12) ft 2(18) ft 2(54) ft 2(27) ft

16 ft^2 48 ft^2 24 ft^2 36 ft^2 108 ft^2 54 ft^2

88 ft^2 198 ft^2

You can determine if a figure is a scale model of the original by

checking to see if eachand everydimension of the scale figure has been

transformed by the same scale factor.

The ratio of the surface areas 88 : 198 4 : 9. is the square of the scale factor.

So the ratio of surface areas equals the square of the scale factor.

• How does the volume of the scale model compare to the
  volume of the actual sculpture?

Vmodel wh Vsculpturewh

4 ft • 2 ft • 6 ft 6 ft • 3 ft • 9 ft

48 ft^3 162 ft^3

Since 48 : 162 8 : 27,

the ratio of the volumes equals

the cube of the scale factor.

2

3

4

9

2

3

2

3

2

3

2

3

2

3

2

3

Remember:

scale factor 

scale model dimension

actual object dimension

9 ft

3 ft

6 ft

6 ft

2 ft

4 ft

Think

278 is the cube of the scale factor.^23