Spatial Reasoning

EXAMPLE 4 Exploring Effects of Changing Dimensions
The radius and height of the cylinder are multiplied
. Describe the effect on the volume.
by 1__
2
original dimensions:
V = π r 2 h
radius and height multiplied by 1__
2 :
V = π r 2 h
= π (6) 2 (12) = π (3) 2 (6)
= 432π m 3 = 54π m 3
Notice that 54π = 1__ (432π). If the radius and height are multiplied by
1__
8 2 ,
the volume is multiplied by ( 1__
2) 3 , or 1__
8 .
4. The length, width, and height of
the prism are doubled. Describe
the effect on the volume.
EXAMPLE 5 Finding Volumes of Composite Three-Dimensional Figures
Find the volume of the composite figure.
Round to the nearest tenth.
The base area of the prism is B = 1__ (6)(8) 2 = 24 m 2 .
The volume of the prism is V = Bh = 24 (9) = 216 m 3 .
The cylinder’s diameter equals the hypotenuse of
the prism’s base, 10 m. So the radius is 5 m.
The volume of the cylinder is V = π r 2 h = π (5) 2 (5) = 125π m 3 .
The total volume of the figure is the sum of the volumes.
V = 216 + 125π ≈ 608.7 m 3
5. Find the volume of the composite
figure. Round to the nearest tenth.
THINK AND DISCUSS
G.CN.2, G.R.1
1. Compare the formula for the volume of a prism with the formula for
the volume of a cylinder.
2. Explain how Cavalieri’s principle relates to the formula for the volume
of an oblique prism.
3. GET ORGANIZED Copy
and complete the graphic
organizer. In each box,
write the formula for
the volume.
700 Chapter 10 Spatial Reasoning