hw5 - padilla (tp5647) HW05 Gilbert (56650) 1 This...

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Unformatted text preview: padilla (tp5647) HW05 Gilbert (56650) 1 This print-out should have 20 questions. Multiple-choice 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 = y about the y-axis between y = 0 and y = 3. 1. V = 10 cu.units 2. V = 13 cu.units 3. V = 11 cu.units 4. V = 12 cu.units 5. V = 9 cu.units correct Explanation: The volume, V , of the solid of revolution generated by rotating the graph of x = f ( y ) about the y-axis between y = a and y = b is given by V = integraldisplay b a f ( y ) 2 dy. When f ( y ) = y and a = 0 , b = 3, therefore, V = integraldisplay b a y 2 dx = bracketleftBig 1 3 y 3 bracketrightBig 3 . Consequently, V = 9 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 = 4 about the y-axis. 1. V = 4 cu. units 2. V = 4 cu. units 3. V = 8 cu. units correct 4. V = 8 cu. units 5. V = 16 3 cu. units 6. V = 16 3 cu. units Explanation: The region rotated about the y-axis is sim- ilar to the shaded region in 4 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 y-axis 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 4 y dy = bracketleftbigg 1 2 y 2 bracketrightbigg 4 . Consequently, V = 8 . 003 10.0 points padilla (tp5647) HW05 Gilbert (56650) 2 Find the volume, V , of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of y = x 2 , x = y 4 about the x-axis. 1. V = 5 12 cu. units 2. V = 1 2 cu. units 3. V = 7 15 cu. units 4. V = 1 2 cu. units 5. V = 7 15 cu. units correct 6. V = 5 12 cu. units Explanation: Since the graphs of y = x 2 , x = y 4 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 x-axis is given by V = integraldisplay 1 braceleftBig ( x 1 / 4 ) 2- ( x 2 ) 2 bracerightBig dx = integraldisplay 1 braceleftBig x 1 2- x 4 bracerightBig dx = bracketleftbigg 2 3 x 3 2- 1 5 x 5 bracketrightbigg 1 . Consequently, V = parenleftBig 2 3- 1 5 parenrightBig = 7 15 cu. units . 004 10.0 points Find the volume, V , of the solid generated by rotating about the x-axis the region en- closed by the graphs of y = sec x, x = 0 , y = 0 , x = 3 ....
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hw5 - padilla (tp5647) HW05 Gilbert (56650) 1 This...

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