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Math 215
Homework Set 7:
§§
16.7 – 17.2
Winter 2008
Most of the following problems are modiﬁed versions of the recommended homework problems from
your text book
Multivariable Calculus
by James Stewart.
16.8a. Find the volume of one of the smaller wedges cut from a sphere of radius 27 by two planes that
intersect along a diameter at an angle of
π/
6
.
16.8b. Find the volume and center of mass of the solid that lies above the cone
z
= 3
±
x
2
+
y
2
and below
the sphere
x
2
+
y
2
+
z
2
= 9
. Assume that the density of the solid is constant.
16.8c. Find the volume of the solid that lies above the cone
ϕ
=
π/
3
and below the sphere
ρ
= 9 cos(
ϕ
)
.
16.8d. Evaluate
²
²
²
B
(3
x
2
+ 3
y
2
+ 3
z
2
)
dV
where
B
is the ball of radius
13
centered at the origin.
16.8e. Find the center of mass of a solid hemisphere of radius
5
if the density at any point in the hemisphere
is proportional to the point’s distance from the
base
of the hemisphere.
16.8f. Do Problems 27–28 of
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 Winter '08
 Fish
 Multivariable Calculus

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