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WORKSHEET 35  Fall 1995
1.
a) Let Ω be the region bounded by the curves
y
=3
−
x
2
,
y
=2
x
,and
x
= 0. Sketch the graphs
labeling the point of intersection in the Frst quadrant.
b) ±ind the area of Ω.
c) Using discs Fnd the volume of hte solid obtained by revolving Ω about the
x
axis.
d) Using shells Fnd the volume of the solid obtained by revolving Ω about the
y
axis.
2. ±ind the volumes of the following solids using calculus.
a) A ball of radius
r
.
b) A right circular cone of radius
r
and height
h
.
c) A right circular cylinder of height
h
and radius
r
.
3. ±ind the volume of the following solids obtained by rotating:
a) the region bounded by
y
=1
/x
,
x
=1,
x
=
y
,
y
= 0 around the
y
axis;
b) the region bounded by
y
=arctan
x
,
x
=0,
y
=
π/
4 around the
y
axis;
c) the region bounded by
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
 Spring '08
 Grether

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