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Unformatted text preview: griffin (ang684) HW05 Gilbert (56650) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points Determine the volume of the right circular cone generated by rotating the line x = 2 y about the yaxis between y = 0 and y = 4. 1. V = 244 3 cu.units 2. V = 253 3 cu.units 3. V = 256 3 cu.units correct 4. V = 247 3 cu.units 5. V = 250 3 cu.units Explanation: The volume, V , of the solid of revolution generated by rotating the graph of x = f ( y ) about the yaxis between y = a and y = b is given by V = integraldisplay b a f ( y ) 2 dy. When f ( y ) = 2 y and a = 0 , b = 4, therefore, V = integraldisplay b a 4 y 2 dx = bracketleftBig 4 3 y 3 bracketrightBig 4 . Consequently, V = 256 3 cu.units . 002 10.0 points Find the volume, V , of the solid obtained by rotating the region bounded by y = x 2 , x = 0 , y = 3 about the yaxis. 1. V = 9 2 cu. units correct 2. V = 3 cu. units 3. V = 3 cu. units 4. V = 9 4 cu. units 5. V = 9 4 cu. units 6. V = 9 2 cu. units Explanation: The region rotated about the yaxis is sim ilar to the shaded region in 3 y x (not drawn to scale). Now the volume of the solid of revolution generated by revolving the graph of x = f ( y ) for a y b about the yaxis is given by volume = integraldisplay b a f ( y ) 2 dy . To apply this we have first to express x as a function of y since initially y is defined in terms of x by y = x 2 . Thus after taking square roots we see that V = integraldisplay 3 y dy = bracketleftbigg 1 2 y 2 bracketrightbigg 3 . Consequently, V = 9 2 . griffin (ang684) HW05 Gilbert (56650) 2 003 10.0 points Find the volume, V , of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of y = x 5 2 , x = y 3 about the xaxis. 1. V = 13 30 cu. units 2. V = 2 5 cu. units 3. V = 7 20 cu. units 4. V = 13 30 cu. units correct 5. V = 2 5 cu. units 6. V = 7 20 cu. units Explanation: Since the graphs of y = x 5 2 , x = y 3 intersect at (0 , 0) and at (1 , 1) the bounded region in the first quadrant enclosed by their graphs is the shaded area shown in 1 1 Thus the volume of the solid of revolution generated by rotating this region about the xaxis is given by V = integraldisplay 1 braceleftBig ( x 1 / 3 ) 2 ( x 5 2 ) 2 bracerightBig dx = integraldisplay 1 braceleftBig x 2 3 x 5 bracerightBig dx = bracketleftbigg 3 5 x 5 3 1 6 x 6 bracketrightbigg 1 . Consequently, V = parenleftBig 3 5 1 6 parenrightBig = 13 30 cu. units . 004 10.0 points Find the volume, V , of the solid generated by rotating about the xaxis the region en closed by the graphs of y = sec x, x = 0 , y = 0 , x = 3 ....
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This note was uploaded on 09/09/2009 for the course M 408L taught by Professor Gilbert during the Spring '09 term at University of TexasTyler.
 Spring '09
 GILBERT

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