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Unformatted text preview: Create assignment, 57321, Homework 11, Apr 19 at 4:32 pm 1 This printout should have 15 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC6b02a 53:02, calculus3, multiple choice, > 1 min, wordingvariable. 001 Find the volume of the frustrum of the right circular cone generated by rotating the line y = x + 3 about the xaxis between x = 0 and x = 2. 1. V = 98 3 π cu.units correct 2. V = 107 3 π cu.units 3. V = 104 3 π cu.units 4. V = 101 3 π cu.units 5. V = 95 3 π cu.units Explanation: The volume, V , of the solid of revolution generated by rotating the graph of y = f ( x ) about the xaxis between x = a and x = b is given by V = π Z b a f ( x ) 2 dx. When f ( x ) = x + 3 and a = 0 , b = 2, there fore, V = π Z 2 ‡ x + 3 · 2 dx = π h 1 3 ‡ x + 3 · 3 i 2 . Consequently, V = 98 3 π cu.units . keywords: volume, integral, solid of revolu tion CalC6b49s 53:02, calculus3, multiple choice, > 1 min, wordingvariable. 002 A cap of a sphere is generated by rotating the shaded region in h y r about the yaxis. Determine the volume, V , of this cap when the radius of the sphere is r = 4 inches and the height of the cap is h = 1 inches. 1. V = 11 3 π cu. ins correct 2. V = 14 3 π cu. ins 3. V = 13 3 π cu. ins 4. V = 4 π cu. ins 5. V = 10 3 π cu. ins Explanation: Create assignment, 57321, Homework 11, Apr 19 at 4:32 pm 2 Since the sphere has radius r = 4 inches, we can think of this sphere as being generated by rotating the circle x 2 + y 2 = 4 2 about the y axis. The cap of the sphere is then generated by rotating the the graph of x = f ( y ) = p 4 2 y 2 on the interval [3 , 4] about the yaxis. Thus the volume of the cap is V = π Z 4 3 f ( y ) 2 dy = π Z 4 3 n 4 2 y 2 o dy = π • 4 2 y 1 3 y 3 ‚ 4 3 . Consequently, V = 11 3 cu. ins. . keywords: volume, integral, solid of revolu tion, integral respect to y CalC6b47s 53:02, calculus3, multiple choice, < 1 min, wordingvariable....
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This note was uploaded on 03/20/2008 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas.
 Spring '06
 McAdam

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