6th Grade Math Textbook, Fundamentals

11

5 in. (^165)
16 in.  slant height
1
5 in. 2 
height
of prism
1
2 in.
1
2 in.
1
2 in.
Remember: Surface Area Formulas
Rectangular Prism: S 2 w 2 h 2 hw
Triangular Prism: S 2 BA 1 A 2 A 3
Pyramid: SBLA
Cylinder: S 2 r^2  2 rh
Cone: Sr^2 r
Remember: Volume Formulas
Rectangular Prism: Vwh
Triangular Prism: VBh
Rectangular Pyramid: V Bh
Triangular Pyramid: V Bh
Cylinder: VBhr^2 h
Cone: V 31 Bh^13 r^2 h
1
3
1
3
5
16 in.
1
5 in. 2
1
2 in.
512 ^112
320 Chapter 11
11-10
Surface Area and Volume of Complex
Three-Dimensional Figures
Objective To draw complex three-dimensional figures• To use nets to find the surface area and
volume of complex three-dimensional figures• To use formulas to find the surface area and volume
of complex three-dimensional figures
A souvenir manufacturer will produce replicas of
the Washington Monument. Replicas will be created
from plastic and then painted with a texture paint.
For each replica, about how many square inches will
be covered by paint?
To answer the question, you need to find the surface
area of complex three-dimensional figures. As with
two-dimensional figures, complex three-dimensional
figures can be constructed by placing two or more
simpler three-dimensional shapes together.

To find the surface area of a complex figure, create

a net. Then find the area of each two-dimensional

figure and calculate the sum of the areas.

To find the surface area of the souvenir, create a net.

Notice that all the figures in this net are polygons.

Area of the triangles: A (^4) ( bh) (^4) [()( )] in.^2
Area of the rectangles: A 4 w (^4) ()( )11 in.^2
Area of the square: As^2 ()
2
 in.^2
Then find the sum of the areas (S) to the nearest 0.1 in.^2
S 11 
 11
11.6 in.^2
So the manufacturer will cover about 11.6 square inches
of each souvenir with paint.

To find the volume of a complex figure, identify which

figures helped to create it. A complex figure can be made

from the unionof two or more three-dimensional figures.

Then, calculate the volume of the complex figure by finding

the sum of the volumesof the figures used to construct it.

1

4

1

4

9

16

5

16

1

2

11

2

1

2

5

16

5

16

1

2

1

2

1

2