Question

Let S be the solid of revolution obtained by revolving the region defined by the curves y = ?x and y = (1/2)x of the x y plane about the line y = -4. We wish to compute the volume of S using the washer method. a) Find the smallest x value x1 and the largest x value x2 of the points in this region. x1 = 0 x2 = 4 b) Let x be a real number in the interval [x1, x2]. The section S of the plane of abscissa x is a washer. What is the inner radius ri and the outer radius re of this washer? ri = re = c) Let x be as in (b) for ?x > 0 small. The volume of the slice delimited by the planes of abscissa x and x + ?x is approximately A(x) ?x. What is the function A(x)? A(x) = Remark: there is no ?x in the answer. Also, keep in mind that ? is written pi. For example, 2? / 3 in Maple is written 2*pi/3. d) Find the volume of S with ±0.001 precision. Answer:

          Let S be the solid of revolution obtained by revolving the region defined by the curves y = ?x and y = (1/2)x of the x y plane about the line y = -4.
We wish to compute the volume of S using the washer method.
a) Find the smallest x value x1 and the largest x value x2 of the points in this region.
x1 = 0
x2 = 4
b) Let x be a real number in the interval [x1, x2].
The section S of the plane of abscissa x is a washer.
What is the inner radius ri and the outer radius re of this washer?
ri =
re =
c) Let x be as in (b) for ?x > 0 small.
The volume of the slice delimited by the planes of abscissa x and x + ?x is approximately A(x) ?x. What is the function A(x)?
A(x) =
Remark: there is no ?x in the answer. Also, keep in mind that ? is written pi. For example, 2? / 3 in Maple is written 2*pi/3.
d) Find the volume of S with ±0.001 precision.
Answer:

Let S be the solid of revolution obtained by revolving the region defined by the curves y = ?x and y = (1/2)x of the x y plane about the line y = -4.
We wish to compute the volume of S using the washer method.
a) Find the smallest x value x1 and the largest x value x2 of the points in this region.
x1 = 0
x2 = 4
b) Let x be a real number in the interval [x1, x2].
The section S of the plane of abscissa x is a washer.
What is the inner radius ri and the outer radius re of this washer?
ri =
re =
c) Let x be as in (b) for ?x > 0 small.
The volume of the slice delimited by the planes of abscissa x and x + ?x is approximately A(x) ?x. What is the function A(x)?
A(x) =
Remark: there is no ?x in the answer. Also, keep in mind that ? is written pi. For example, 2? / 3 in Maple is written 2*pi/3.
d) Find the volume of S with ±0.001 precision.
Answer:

Added by Joaquin G.

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