nanni (arn437) – Assignment 8 – guntel – (54940)
1
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8
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001
10.0points
Find the volume,
V
, of the solid obtained
by rotating the bounded region in the first
quadrant enclosed by the graphs of
y
=
x
2
,
x
=
y
2
about the
x
axis.
1.
V
=
2
5
π
2.
V
=
3
5
π
3.
V
=
1
5
π
4.
V
=
3
10
π
correct
5.
V
=
1
2
π
Explanation:
Since the graphs of
y
=
x
2
,
x
=
y
2
intersect in the first quadrant at (0
,
0) and at
(1
,
1) the bounded region in the first quad
rant enclosed by their graphs is the shaded
area shown in
1
1
Thus the volume of the solid of revolution
generated by rotating this region about the
x
axis is given by
V
=
π
integraldisplay
1
0
braceleftBig
(
x
1
/
2
)
2

(
x
2
)
2
bracerightBig
dx
=
π
integraldisplay
1
0
braceleftBig
x
1

x
4
bracerightBig
dx
=
π
bracketleftbigg
1
2
x
2

1
5
x
5
bracketrightbigg
1
0
.
Consequently,
V
=
π
parenleftBig
1
2

1
5
parenrightBig
=
3
10
π
.
002
10.0points
Find the volume,
V
, of the solid obtained
by rotating the region bounded by the graphs
of
x
=
y
2
,
x
=
√
y
about the line
x
=

1.
1.
V
=
2
π
5
2.
V
=
3
π
4
3.
V
=
7
π
15
4.
V
=
3
π
5
5.
V
=
29
π
30
correct
6.
V
=
9
π
10
7.
V
=
π
2
8.
V
=
31
π
30
Explanation:
The region enclosed by the graphs of
x
=
√
y,
x
=
y
2
,
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nanni (arn437) – Assignment 8 – guntel – (54940)
2
is the shaded region in
y
x
x
=
√
y
:
x
=
y
2
:
(1
,
1)
To determine the volume of the solid gener
ated when this region is rotated about the
line
x
=

1 let’s see first what a horizontal
crosssection of the solid looks like. As shown
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 Fall '11
 GUNTEL
 cu. ins

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