2. A solid is created by rotating the region bounded by x=y, x=8, and the z-axis, about the z-axis. (a) Draw the solid, and draw an example cylindrical shell. Your cylinders will be horizontal now. Label the point where the cylinder touches the curve as (x, y). Find a variable or an expression which represents the radius of the cylinder. Radius= Find a variable or an expression which represents the height (here it looks more like "length"). Height = How might we represent the thickness of the cylinder? Thickness= Use constraints to get all of these quantities in terms of the same variable. (b) Find equations for the surface area and volume of your cylindrical shell. Acyl Veyl (e) Find appropriate bounds and integrate to calculate the total volume of the solid.
2. A solid is created by rotating the region bounded by x=y, x=8, and the z-axis, about the z-axis. (a) Draw the solid, and draw an example cylindrical shell. Your cylinders will be horizontal now. Label the point where the cylinder touches the curve as (x, y). Find a variable or an expression which represents the radius of the cylinder. Radius= Find a variable or an expression which represents the height (here it looks more like "length"). Height = How might we represent the thickness of the cylinder? Thickness= Use constraints to get all of these quantities in terms of the same variable. (b) Find equations for the surface area and volume of your cylindrical shell. Acyl Veyl (e) Find appropriate bounds and integrate to calculate the total volume of the solid.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:2. A solid is created by rotating the region bounded by x=y, x=8, and the z-axis, about the z-axis.
E
(a) Draw the solid, and draw an example cylindrical shell. Your cylinders will be horizontal now.
Label the point where the cylinder touches the curve as (x, y).
Find a variable or an expression which represents the radius of the cylinder.
Radius=
Find a variable or an expression which represents the height (here it looks more like "length").
Height =
How might we represent the thickness of the cylinder?
Thickness ==
Use constraints to get all of these quantities in terms of the same variable.
(b) Find equations for the surface area and volume of your cylindrical shell.
Acyl ==
Veyl=
(e) Find appropriate bounds and integrate to calculate the total volume of the solid.
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