the parabola
y
=
x:1tothePlUUJolay
=
2 
x'l.
,
o
x
3.
The
solid lies
between
planes perpendicular
to
the
xaxis
at
x


1
and
x 
I.
The
crosssections perpendicular
to
the xaxis
between
these planes
arc
squares whose bases
run
from
the
semi
circle
y
= 
~
to
the semicircle
y
=
~.
4.
The
solid
lies
benwen
planes perpendicular
to
the xaxis
at
x
=
I
and
x
=
1.
The
crosssections perpendicular
to
the
xaxis
be
tween
these planes
~s
whose
diagonals
run
from
the
semicircley
=
VI

x
2
to
the
semicircley
=
~.
5.
The
base
of
a solid
is
the
:region
between
the
ClU'Ve
y
=
2
~
and
the
interval
[0,
'Ir]
on
the xaxis.
The
crosssections perpendi
cular
to
the xaxis
are
L
cquilateIal.
triangles with bases
running
from.
the
xaxis
to
the
curve
as
shown
in
the accompanying figure.
•
x
b. squares with bases
running
from
the xaxis
to
the curve.
6.
The
solid lies between planes
perpendi.cular
to
the
xaxis
at
x

'lr/3
andx

'lr/3.
The
crosssections perpendicular to the
xaxis
are
L
circula:r
disks with diameters
running
from
the
curve
Y

tanxtothecurvey

secx.
b. squares whose bases
run
from
the
curve
Y

tan
x
to the
curvey

secx.
7.
The
base
of
a solid
is
the
region
bounded
by
the
graphs
of
Y

3x,
Y

6,
and
x

O.
The
crosssections perpendicular
to
the
xaxis
arc
L
rectangles
of
height
10.
b. rectangles
of
perimeter
20.
8.
The
base
of
a solid is the region
bmmded by
the
graphs
of
Y

v';;
and
Y

x12.
The
crosssections perpendicular
to
the
xaxis
are
L
isosceles triangles
of
height
6.
b.
semicircles
with
diameters
running
across
the
base
of
the
solid
9.
The
solid lies
between
planes perpendicular
to
the
yaxis
at
y
=
0
and
y
=
2.
The
crosssections perpendicular
to
the
yaxis arc cir
cular
disks with
diamebml
running
from
the
yaxis
to
the parabola
x
_
Vsy2.
10.
The
base
of
the solid is
the
diskx
2
+
y:1
S L
The
crosssections
by
planes perpendicular
to
the
yaxis
between
y
= 
1
and
y
=
1
arc isosceles
right
triangles with
one
leg
in
the disk.
,

~
o
11.
Find
the
volume
ofthc
given
tetrahedron.
(Hint
Consider
slices
perpendicular
to
one
of
tile
labeled edges.)
,
,
/
11.
Find
the volume
of
the
given
pyramid,
which
has
a square
base
of
area
9
and
height
5.
13. A twisted
lOUd
A
square
of
side
length
s
lies
in
a
plane
perpen
dicularto
alineL.
One
vertex
of
the square lies
onL.
As
this
square
moves
a
distance
II
along
L,
the
square
turns
one
revolution
about
L
to
generate
a carkscrewli]re colmnn
with square
crosssections.
L
Find
the volmne
of
the colmnn.
b.
What
will
the
volume
be
if
the
square
turns twice instead
of
once?
Give
reasons foryom
answer.
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Expert Verified
14.
CJIYlIlisi'.
principle
A solid lies
between
planes perpendicular
to
the xaxis
at
x 
0
and
x 
12. The crosssections
by
planes
perpendicular
to
the
xaxis
are circular
disks whose diameters
run
from
the line
y

x/2
to the line
y

x
as shawn
in
the accompa
nying
figure.