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2) Region R, that is bounded by the graph y = 2+√√,,x=1 and y=2, is revolved about the line y=1 to form a solid of revolution. Answer the following questions: a) Sketch the region R b) What is the radius of the cylindrical shell? What is the height of the cylindrical shell? (in terms of x and/or y) c) Determine the direction/orientation of the cross-sections and then determine whether we are using dx or dy for the thickness. d) What is the expression of the surface area of the cylindrical shell in terms of x and/ory (can be determined from part c)? f) Set up the integral to calculate the volume of the solid. (Do not need to evaluate the integral)

2) Region R, that is bounded by the graph y = 2+√√,,x=1 and y=2, is revolved about the line y=1 to form a solid of revolution. Answer the following questions: a) Sketch the region R b) What is the radius of the cylindrical shell? What is the height of the cylindrical shell? (in terms of x and/or y) c) Determine the direction/orientation of the cross-sections and then determine whether we are using dx or dy for the thickness. d) What is the expression of the surface area of the cylindrical shell in terms of x and/ory (can be determined from part c)? f) Set up the integral to calculate the volume of the solid. (Do not need to evaluate the integral)

Advanced Engineering Mathematics
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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Week 05 Participation Questions (1 of 2) All Sections For this section, the main idea is to set up the volume of a cylindrical shell whose volume can be calculated by the formula (surface area of the cylinder shell)* (thickness). Thickness can be expressed as dx or dy depending on the orientation of the solid. The key step is to set up the surface area of the cylinder. (Recall that the surface area of a cylinder is 2*pi*radius*height). Consider the following solids: on R, that is bounded by the graph y = 2+√√x,, x=1 and y=2, is questions. a, ch R. b) What is th c) Determine the directi d) What is ession of the surface area of the cal shell in terms or x et up the integral to calculate the volume of the solid. (Do not need to evaluate the integral) Lr Vli .entatic What is oss-sec¹ is ar of the c de atne line x=1 to form a solid of revoi al cl ...ne whe (P er w ms of x- using dx or dy for the thickness. ed from part c)? following V 2) Region R, that is bounded by the graph y = 2 + √√x,, x= 1 and y=2, is revolved about the line y=1 to form a solid of revolution. Answer the following questions: a) Sketch the region R b) What is the radius of the cylindrical shell? What is the height of the cylindrical shell? (in terms of x and/or y) c) Determine the direction/orientation of the cross-sections and then determine whether we are using dx or dy for the thickness. d) What is the expression of the surface area of the cylindrical shell in terms of x and/or y (can be determined from part c)? f) Set up the integral to calculate the volume of the solid. (Do not need to evaluate the integral)
Transcribed Image Text:Week 05 Participation Questions (1 of 2) All Sections For this section, the main idea is to set up the volume of a cylindrical shell whose volume can be calculated by the formula (surface area of the cylinder shell)* (thickness). Thickness can be expressed as dx or dy depending on the orientation of the solid. The key step is to set up the surface area of the cylinder. (Recall that the surface area of a cylinder is 2*pi*radius*height). Consider the following solids: on R, that is bounded by the graph y = 2+√√x,, x=1 and y=2, is questions. a, ch R. b) What is th c) Determine the directi d) What is ession of the surface area of the cal shell in terms or x et up the integral to calculate the volume of the solid. (Do not need to evaluate the integral) Lr Vli .entatic What is oss-sec¹ is ar of the c de atne line x=1 to form a solid of revoi al cl ...ne whe (P er w ms of x- using dx or dy for the thickness. ed from part c)? following V 2) Region R, that is bounded by the graph y = 2 + √√x,, x= 1 and y=2, is revolved about the line y=1 to form a solid of revolution. Answer the following questions: a) Sketch the region R b) What is the radius of the cylindrical shell? What is the height of the cylindrical shell? (in terms of x and/or y) c) Determine the direction/orientation of the cross-sections and then determine whether we are using dx or dy for the thickness. d) What is the expression of the surface area of the cylindrical shell in terms of x and/or y (can be determined from part c)? f) Set up the integral to calculate the volume of the solid. (Do not need to evaluate the integral)
Expert Solution
Step 1: Determine the given variables

We have given a region R enclosed by different curves. Using this graph, we have to determine different things.

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