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Math 152
Workshop 2
Spring 2011
1. Let
R
be the parabolic region in the
x

y
plane bounded below by the curve
y
=
x
2
and above
by the line
y
= 1.
(a) Sketch
R
. Set up and evaluate an integral that gives the area of
R
.
(b) Suppose a solid has base
R
and the crosssections of the solid perpendicular to the
y
axis
are squares. Sketch the solid and ﬁnd its volume.
(c) Suppose a solid has base
R
and the crosssections of the solid perpendicular to the
y
axis
are equilateral triangles. Sketch the solid and ﬁnd its volume.
2. Start with the region
A
in the ﬁrst quadrant enclosed by the
x
axis and the parabola
y
=
2
x
(2

x
). Then obtain solids of revolution
S
1
,
S
2
, and
S
3
by revolving
A
about the lines
y
= 4
,
y
=

2
,
and
x
= 4
respectively. All three solids are (unusual) “doughnuts” which are 8 units across, whose hole
is 4 units across, and whose height is 2 units. Sketch them.
(a) Which do you expect to have larger volume,
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This note was uploaded on 01/10/2012 for the course CALCULUS 152 taught by Professor Sosa during the Spring '11 term at Rutgers.
 Spring '11
 SOSA

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