Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? + y = 9 (in the ry-plane), and whose vertical cross-sections are rectangles of height r| and length y = 2/9- a2 (from r = -3 to a = 3). Here is a rough sketch of a cross-section (not drawn to scale). |x| x-axis у-ахis (d) Suppose instead that the height of the cross-sectional rectangle at r is 3– a from a = -3 to r = 3. (i) Sketch the new figure, indicating 3 different cross-sections in your sketch. (ii) Express the volume as an integral using the method of slicing (without computing the value). (iii) Using symmetry, express the volume as an integral of the form where C is a constant. Find C and briefly explain why you can do this. (iv) Compute the volume.
Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? + y = 9 (in the ry-plane), and whose vertical cross-sections are rectangles of height r| and length y = 2/9- a2 (from r = -3 to a = 3). Here is a rough sketch of a cross-section (not drawn to scale). |x| x-axis у-ахis (d) Suppose instead that the height of the cross-sectional rectangle at r is 3– a from a = -3 to r = 3. (i) Sketch the new figure, indicating 3 different cross-sections in your sketch. (ii) Express the volume as an integral using the method of slicing (without computing the value). (iii) Using symmetry, express the volume as an integral of the form where C is a constant. Find C and briefly explain why you can do this. (iv) Compute the volume.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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Transcribed Image Text:Problem 2: Let F be the 3-dimensional figure whose base is the region bounded by the circle a? +y? = 9
(in the ry-plane), and whose vertical cross-sections are rectangles of height |r| and length y = 2v9 – a2
(from r = -3 to x = 3). Here is a rough sketch of a cross-section (not drawn to scale).
|x|
x-axIS
y-axis
(d) Suppose instead that the height of the cross-sectional rectangle at r is 3 – a from r = -3 to r = 3.
(i) Sketch the new figure, indicating 3 different cross-sections in your sketch.
(ii) Express the volume as an integral using the method of slicing (without computing the value).
(iii) Using symmetry, express the volume as an integral of the form
/9-a2 da
where C is a constant. Find C and briefly explain why you can do this.
(iv) Compute the volume.
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