mao (tm23477) – HW05 – Radin – (56570)
1
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22
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before answering.
001
10.0 points
Determine the volume of the right circular
cone generated by rotating the line
x
=
4
5
y
about the
y
axis between
y
= 0 and
y
= 3.
1.
V
=
144
25
π
cu.units
2.
V
=
94
25
π
cu.units
3.
V
=
169
25
π
cu.units
4.
V
=
69
25
π
cu.units
5.
V
=
119
25
π
cu.units
002
10.0 points
Find the volume of the paraboloid gener
ated by rotating the graph of
y
= 4
√
x
be
tween
x
= 0 and
x
= 1 about the
x
axis.
1.
volume = 8
π
cu.units
2.
volume = 9
π
cu.units
3.
volume = 11
π
cu.units
4.
volume = 7
π
cu.units
5.
volume = 10
π
cu.units
003
10.0 points
Find the volume,
V
, of the solid obtained
by rotating the region bounded by
y
=
x
2
,
x
= 0
,
y
= 16
about the
y
axis. (Hint:
as always graph the
region first
).
1.
V
= 128 cu. units
2.
V
= 64
π
cu. units
3.
V
= 64 cu. units
4.
V
= 128
π
cu. units
5.
V
=
256
3
π
cu. units
6.
V
=
256
3
cu. units
004
10.0 points
Let
A
be the bounded region in the first
quadrant enclosed by the graphs of
f
(
x
) =
x ,
g
(
x
) =
x
3
.
Find the volume of the solid obtained by ro
tating the region
A
about the line
x
+ 3 = 0
.
1.
volume =
23
30
π
2.
volume =

37
30
π
3.
volume =
53
30
π
4.
volume =
83
30
π
5.
volume =

7
30
π
005
10.0 points
A cap of a sphere is generated by rotating
the shaded region in
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mao (tm23477) – HW05 – Radin – (56570)
2
y
2
4
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.
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 Spring '10
 RAdin

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