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Volumes by Shell Method
Grade Level
Calculus I
CAL1.130 Volumes by Shell Method
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Use cylindrical shells. The first-quadrant region bounded by x=8-y
2
, x=2y, and the x-axis is rotated about the line y=4. Which setup and volume are correct?
A
pi*integral_{0}
2
(4 - y)*(-y
2
- 2*y + 8) dy; V = 92*pi/3
B
2*pi*integral_{0}
2
(4 - y)*(-y
2
- 2*y + 8) dy; V = 184*pi/3
C
2*pi*integral_{0}
2
(y)*(-y
2
- 2*y + 8) dy; V = 40*pi/3
D
2*pi*integral_{0}
2
(4 - y)*(8 - y
2
) dy; V = 248*pi/3
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