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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 37E
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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.
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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