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1. Area of the region outside the circle x² + y² = 4 but inside the ellipse (a) horizontal strips (b) vertical strips 2² y² = 1 using

1. Area of the region outside the circle x² + y² = 4 but inside the ellipse (a) horizontal strips (b) vertical strips 2² y² = 1 using

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 7E: The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of...
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II. PROBLEM SOLVING SET-UP the definite integral that will solve the area or volume described in each item. You may take advantage of symmetry whenever applicable. 1. Area of the region outside the circle x² + y² = 4 but inside the ellipse + = 1 using 2² y² 9 4 (a) horizontal strips (b) vertical strips 2. Volume of the solid (of revolution) obtained by rotating the region in item 1 about the y-axis using (a) disks (b) cylindrical shells. Warning: Avoid double counting. 3. Imagine an original glazed doughnut whose diameter (measured between the outside edges) is 75 mm while its hole (measured between the inside edges) has diameter 11 mm. (a) Assuming that the cross section of this doughnut is a perfect circle, explicitly state an equation that describes such circle. Hint 1: Equation of a circle is (rh)² + (y-k)² = r² where r is its radius while (h, k) is the location of its center.. Hint 2: The radius of the circular cross-section can be deduced from the given dimension. (b) To obtain a doughnut, the circle in item 3a will be revolved about an axis. Set-up the definite integral that will give the volume of the doughnut using disks. cylindrical shells.
Transcribed Image Text:II. PROBLEM SOLVING SET-UP the definite integral that will solve the area or volume described in each item. You may take advantage of symmetry whenever applicable. 1. Area of the region outside the circle x² + y² = 4 but inside the ellipse + = 1 using 2² y² 9 4 (a) horizontal strips (b) vertical strips 2. Volume of the solid (of revolution) obtained by rotating the region in item 1 about the y-axis using (a) disks (b) cylindrical shells. Warning: Avoid double counting. 3. Imagine an original glazed doughnut whose diameter (measured between the outside edges) is 75 mm while its hole (measured between the inside edges) has diameter 11 mm. (a) Assuming that the cross section of this doughnut is a perfect circle, explicitly state an equation that describes such circle. Hint 1: Equation of a circle is (rh)² + (y-k)² = r² where r is its radius while (h, k) is the location of its center.. Hint 2: The radius of the circular cross-section can be deduced from the given dimension. (b) To obtain a doughnut, the circle in item 3a will be revolved about an axis. Set-up the definite integral that will give the volume of the doughnut using disks. cylindrical shells.
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