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1 HW 7.3 MATH 202 ( ) Question Question Details SEssCalc [ ] Let S be the solid obtained by rotating the region shown in the figure about the yaxis. (Assume a = 12 and b = 4.) Sketch a typical approximating shell. 1/12

2 Find its circumference c and height h. c(x) = h(x) = Use shells to find the volume V of S. 2. Question Details SEssCalc [ ] Let S be the solid obtained by rotating the region shown in the figure about the yaxis. (Assume a = 8 and b = 2.) Sketch a typical approximating shell. 2/12

3 What are its circumference c and height h? c(x) = h(x) = Use shells to find the volume V of S. 3. Question Details SEssCalc MI. [ ] Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the yaxis. y = 7e x2, y = 0, x = 0, x = 1 Sketch the region and a typical shell. 3/12

4 4/12

5 4. Question Details SEssCalc [ ] Let V be the volume of the solid obtained by rotating about the yaxis the region bounded by slicing. y = 25x and y = x Find V Draw a diagram to explain your method. Find V by cylindrical shells. Draw a diagram to explain your method. 5/12

6 5. Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the xaxis. xy = 3, x = 0, y = 3, y = 5 3 xy = 3 x =, so y 5 3 2π y dy 3 y 5 5 = 2π 3 dy = 2π 3y 3 3 = 2π(15 9) = 12π 6/12

7 6. Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the xaxis. y = x 3, y = 27, x = 0 Sketch the region and a typical shell. 7. Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the xaxis. 7/12

8 x = 12y 2 4y 3, x = 0 Sketch the region and a typical shell /12

9 Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the xaxis. x = 1 + (y 5) 2, x = 10 Sketch the region and a typical shell. 9/12

10 9. Question Details SEssCalc MI. [ ] Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about x = 3. y = 5x 4, y = 0, x = Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the xaxis. x + y = 3, x = 4 (y 1) 2 Sketch the region and a typical shell. 10/12

11 11. Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 2, y = 0, x = 1; about x = 2 x 12. Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 12x x 2, y = 32; about x = /12

12 13. Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 8 x 2, y = x 2 ; about x = Question Details SEssCalc [ ] Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 8. 27y = x 3, y = 0, x = 6 Assignment Details Name (AID): HW 7.3 MATH 202 ( ) Submissions Allowed: 5 Category: Homework Code: Locked: No Author: Islam, Mohammad ( shafiqusa@gmail.com ) Last Saved: Mar 28, :22 AM EDT Permission: Protected Randomization: Person Which graded: Last Feedback Settings Before due date Question Score Assignment Score Publish Essay Scores Question Part Score Mark Add Practice Button Help/Hints Response Save Work After due date Question Score Assignment Score Publish Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response 12/12