yp968 – Homework 4 – Radin – (58415)
1
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printout
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have
20
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001
10.0 points
Find the volume,
V
, of the solid obtained
by rotating the region bounded by
y
=
1
x
,
x
= 2
,
x
= 3
,
y
= 0
about the
x
axis.
1.
V
=
1
6
π
2.
V
=
1
6
3.
V
=
1
24
π
4.
V
=
1
12
5.
V
=
1
24
6.
V
=
1
12
π
002
10.0 points
Find the volume,
V
, of the solid obtained
by rotating the bounded region in the first
quadrant enclosed by the graphs of
y
=
x
3
2
,
x
=
y
4
about the
x
axis.
1.
V
=
1
2
π
cu. units
2.
V
=
1
2
cu. units
3.
V
=
5
12
π
cu. units
4.
V
=
7
15
cu. units
5.
V
=
7
15
π
cu. units
6.
V
=
5
12
cu. units
003
10.0 points
Find the volume,
V
, of the solid formed by
rotating the region bounded by the graphs of
y
=
√
x
+ 5
,
y
= 5
,
x
= 0
,
x
= 1
about the line
y
= 3.
1.
V
=
19
6
π
cu. units
2.
V
=
11
3
π
cu. units
3.
V
=
23
6
π
cu. units
4.
V
=
10
3
π
cu. units
5.
V
=
7
2
π
cu. units
004
10.0 points
A cap of a sphere is generated by rotating
the shaded region in
y
2
4
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yp968 – Homework 4 – Radin – (58415)
2
about the
y
axis.
Determine the volume of
this cap when the radius of the sphere is 4
inches and the height of the cap is 2 inches.
1.
volume =
43
3
π
cu. ins
2.
volume =
40
3
π
cu. ins
3.
volume = 14
π
cu. ins
4.
volume =
44
3
π
cu. ins
5.
volume =
41
3
π
cu. ins
005
10.0 points
The volume of a solid can often be deter
mined by integration even when the cross
section of the solid is not necessarily a circle.
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 Spring '08
 RAdin
 Logarithm

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