<s>
In	O
geometry	O
and	O
science	O
,	O
a	O
cross	B-Application
section	I-Application
is	O
the	O
non-empty	O
intersection	O
of	O
a	O
solid	O
body	O
in	O
three-dimensional	O
space	O
with	O
a	O
plane	O
,	O
or	O
the	O
analog	O
in	O
higher-dimensional	O
spaces	O
.	O
</s>
<s>
Cutting	O
an	O
object	O
into	O
slices	O
creates	O
many	O
parallel	O
cross-sections	B-Application
.	O
</s>
<s>
The	O
boundary	O
of	O
a	O
cross-section	B-Application
in	O
three-dimensional	O
space	O
that	O
is	O
parallel	O
to	O
two	O
of	O
the	O
axes	O
,	O
that	O
is	O
,	O
parallel	O
to	O
the	O
plane	O
determined	O
by	O
these	O
axes	O
,	O
is	O
sometimes	O
referred	O
to	O
as	O
a	O
contour	O
line	O
;	O
for	O
example	O
,	O
if	O
a	O
plane	O
cuts	O
through	O
mountains	O
of	O
a	O
raised-relief	O
map	O
parallel	O
to	O
the	O
ground	O
,	O
the	O
result	O
is	O
a	O
contour	O
line	O
in	O
two-dimensional	O
space	O
showing	O
points	O
on	O
the	O
surface	O
of	O
the	O
mountains	O
of	O
equal	O
elevation	O
.	O
</s>
<s>
In	O
technical	B-Application
drawing	I-Application
a	O
cross-section	B-Application
,	O
being	O
a	O
projection	O
of	O
an	O
object	O
onto	O
a	O
plane	O
that	O
intersects	O
it	O
,	O
is	O
a	O
common	O
tool	O
used	O
to	O
depict	O
the	O
internal	O
arrangement	O
of	O
a	O
3-dimensional	O
object	O
in	O
two	O
dimensions	O
.	O
</s>
<s>
It	O
is	O
traditionally	O
crosshatched	O
with	O
the	O
style	O
of	O
crosshatching	B-Application
often	O
indicating	O
the	O
types	O
of	O
materials	O
being	O
used	O
.	O
</s>
<s>
With	O
computed	O
axial	O
tomography	O
,	O
computers	O
can	O
construct	O
cross-sections	B-Application
from	O
x-ray	B-Library
data	O
.	O
</s>
<s>
If	O
a	O
plane	O
intersects	O
a	O
solid	O
(	O
a	O
3-dimensional	O
object	O
)	O
,	O
then	O
the	O
region	O
common	O
to	O
the	O
plane	O
and	O
the	O
solid	O
is	O
called	O
a	O
cross-section	B-Application
of	O
the	O
solid	O
.	O
</s>
<s>
A	O
plane	O
containing	O
a	O
cross-section	B-Application
of	O
the	O
solid	O
may	O
be	O
referred	O
to	O
as	O
a	O
cutting	O
plane	O
.	O
</s>
<s>
The	O
shape	O
of	O
the	O
cross-section	B-Application
of	O
a	O
solid	O
may	O
depend	O
upon	O
the	O
orientation	O
of	O
the	O
cutting	O
plane	O
to	O
the	O
solid	O
.	O
</s>
<s>
For	O
instance	O
,	O
while	O
all	O
the	O
cross-sections	B-Application
of	O
a	O
ball	O
are	O
disks	O
,	O
the	O
cross-sections	B-Application
of	O
a	O
cube	O
depend	O
on	O
how	O
the	O
cutting	O
plane	O
is	O
related	O
to	O
the	O
cube	O
.	O
</s>
<s>
If	O
the	O
cutting	O
plane	O
is	O
perpendicular	O
to	O
a	O
line	O
joining	O
the	O
centers	O
of	O
two	O
opposite	O
faces	O
of	O
the	O
cube	O
,	O
the	O
cross-section	B-Application
will	O
be	O
a	O
square	O
,	O
however	O
,	O
if	O
the	O
cutting	O
plane	O
is	O
perpendicular	O
to	O
a	O
diagonal	O
of	O
the	O
cube	O
joining	O
opposite	O
vertices	O
,	O
the	O
cross-section	B-Application
can	O
be	O
either	O
a	O
point	O
,	O
a	O
triangle	O
or	O
a	O
hexagon	O
.	O
</s>
<s>
Thus	O
,	O
a	O
plane	O
section	O
is	O
the	O
boundary	O
of	O
a	O
cross-section	B-Application
of	O
a	O
solid	O
in	O
a	O
cutting	O
plane	O
.	O
</s>
<s>
A	O
cross	B-Application
section	I-Application
of	O
a	O
polyhedron	O
is	O
a	O
polygon	B-General_Concept
.	O
</s>
<s>
Any	O
cross-section	B-Application
passing	O
through	O
the	O
center	O
of	O
an	O
ellipsoid	O
forms	O
an	O
elliptic	O
region	O
,	O
while	O
the	O
corresponding	O
plane	O
sections	O
are	O
ellipses	O
on	O
its	O
surface	O
.	O
</s>
<s>
A	O
cross-section	B-Application
of	O
a	O
solid	O
right	O
circular	O
cylinder	O
extending	O
between	O
two	O
bases	O
is	O
a	O
disk	O
if	O
the	O
cross-section	B-Application
is	O
parallel	O
to	O
the	O
cylinder	O
's	O
base	O
,	O
or	O
an	O
elliptic	O
region	O
(	O
see	O
diagram	O
at	O
right	O
)	O
if	O
it	O
is	O
neither	O
parallel	O
nor	O
perpendicular	O
to	O
the	O
base	O
.	O
</s>
<s>
Cavalieri	O
's	O
principle	O
states	O
that	O
solids	O
with	O
corresponding	O
cross-sections	B-Application
of	O
equal	O
areas	O
have	O
equal	O
volumes	O
.	O
</s>
<s>
The	O
cross-sectional	B-Application
area	I-Application
(	O
)	O
of	O
an	O
object	O
when	O
viewed	O
from	O
a	O
particular	O
angle	O
is	O
the	O
total	O
area	O
of	O
the	O
orthographic	O
projection	O
of	O
the	O
object	O
from	O
that	O
angle	O
.	O
</s>
<s>
In	O
analogy	O
with	O
the	O
cross-section	B-Application
of	O
a	O
solid	O
,	O
the	O
cross-section	B-Application
of	O
an	O
-dimensional	O
body	O
in	O
an	O
-dimensional	O
space	O
is	O
the	O
non-empty	O
intersection	O
of	O
the	O
body	O
with	O
a	O
hyperplane	O
(	O
an	O
-dimensional	O
subspace	O
)	O
.	O
</s>
<s>
For	O
instance	O
,	O
if	O
a	O
four-dimensional	O
object	O
passed	O
through	O
our	O
three-dimensional	O
space	O
,	O
we	O
would	O
see	O
a	O
three-dimensional	O
cross-section	B-Application
of	O
the	O
four-dimensional	O
object	O
.	O
</s>
<s>
This	O
dynamic	O
object	O
(	O
from	O
the	O
point	O
of	O
view	O
of	O
3-space	O
)	O
is	O
a	O
sequence	O
of	O
cross-sections	B-Application
of	O
the	O
4-ball	O
.	O
</s>
<s>
In	O
geology	O
,	O
the	O
structure	O
of	O
the	O
interior	O
of	O
a	O
planet	O
is	O
often	O
illustrated	O
using	O
a	O
diagram	O
of	O
a	O
cross-section	B-Application
of	O
the	O
planet	O
that	O
passes	O
through	O
the	O
planet	O
's	O
center	O
,	O
as	O
in	O
the	O
cross-section	B-Application
of	O
Earth	O
at	O
right	O
.	O
</s>
<s>
Cross-sections	B-Application
are	O
often	O
used	O
in	O
anatomy	O
to	O
illustrate	O
the	O
inner	O
structure	O
of	O
an	O
organ	O
,	O
as	O
shown	O
at	O
the	O
left	O
.	O
</s>
<s>
A	O
cross-section	B-Application
of	O
a	O
tree	O
trunk	O
,	O
as	O
shown	O
at	O
left	O
,	O
reveals	O
growth	O
rings	O
that	O
can	O
be	O
used	O
to	O
find	O
the	O
age	O
of	O
the	O
tree	O
and	O
the	O
temporal	O
properties	O
of	O
its	O
environment	O
.	O
</s>
