homework3 - solid CONTINUE TO THE NEXT PAGE Math 1120 Fall...

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Math 1120 Homework 3 Due 9/15 or 9/16, 2011 Name: GRADES Book questions / 8 Presentation questions / 30 Print out these pages. Answer the “presentation questions” in the spaces provided. Include full explanations and write your answers in complete, mathematically and grammatically correct sentences. Your answers will be assessed for style and accuracy; you will be given written feedback on these prob- lems. Write your answers to the “book questions” on separate paper and staple to these pages. They will be assessed only for completeness. Always write neatly and legibly. Book questions — 6.1: 2, 8, 44, 46 6.2: 4, 14, 24, 34 Presentation questions 1. [10 points] A solid has as its base a circle of radius 3 and its cross–sections, per- pendicular to the base, are squares standing on the base. What is the volume of the
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Unformatted text preview: solid? CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 3 — due 9/15 or 9/16 2 2. [10 points] (6.1: 55) The volume of a torus. The disk x 2 + y 2 ≤ a 2 is revolved about the line x = b (where b > a ) to generate a solid shaped like a doughnut, known as a torus . Find its volume. ( Hint: i a-a r a 2-y 2 dy = πa 2 / 2 , since it is the area of a semicircle of radius a . ) CONTINUE TO THE NEXT PAGE. Math 1120, Fall 2011 Homework 3 — due 9/15 or 9/16 3 3. [10 points] Let S be the solid obtained by rotating about the y –axis the region enclosed by the curves y = x and y = x 4 . (a) Sketch the region, the solid, and draw a typical disk, washer or cylindrical shell — whichever you prefer to use to Fnd the volume. (b) ±ind the volume of S . THIS IS THE LAST PAGE....
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This note was uploaded on 10/31/2011 for the course MATH 1120 at Cornell.

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homework3 - solid CONTINUE TO THE NEXT PAGE Math 1120 Fall...

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