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Homework for Chapter 6.3: Volumes by Shells
For the problems that involve a little bit of numeric computation,
feel free to use Excel or some other similar program.
As before, you need only turn in the problems that have no answer
in the back of the book.
Drill problems:
4 y=x^2, y=0, x=1
10 x=sqrt(y), x=0, y=1
22 y=x, y=4x-x^2, around the line x=7
24 y=1/(1+x^2), y=0, x=0, x=2; around the line x=2
28 volume from a graph
30 2 pi int_0^2 y/(1+y^2) dy
Applied problems:
44 solid torus like in Ch. 6.2 exercise 63
46 two napkin rings
Question A:
A satellite receiver dish for a network like DirecTV is about 50cm across
and 25 cm deep.
It's not a perfect parabola shape, but we will approximate
it with a nice parabola.
Suppose it's defined by rotating the region
between the following functions around the y-axis (all units in cm):
front surface: y=x^2 / 25 + 1
back surface:
y=x^2 / 25 - 1
for x from 0 to +25.
a) Compute the volume of the plastic that makes up the dish by doing an

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