MATH 233 Midterm: ExamNote4
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Calculus
Assignment
Name___________________________________ ID: 1
Date________________ Period____
-1-
For each problem, use the method of cylindrical shells to find the volume of the solid that
results when the region enclosed by the curves is revolved about the given axis.
1) x = y − 2, x = y − 2
2
Axis: x = 2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
2) x = y3, x = 0, y = 1
Axis: x = 4
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
3) x = 1, x =
(
y − 4
)
2, y = 4, y = 5
Axis: x = 4
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
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Worksheet by Kuta Software LLC
-2-
4) x = 1, x = y − 2, y = 2
Axis: x = −1
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
5) x = 1, x = y3, y = 0
Axis: x = 5
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
6) x = 6 − y, x = 0, y = 2
Axis: x = 5
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
7) x = 1, x =
(
y − 3
)
2, y = 3, y = 4
Axis: x = −1
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
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find more resources at oneclass.com
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-3-
8) x = 1, x = y3, y = 0
Axis: x = −2
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
9) x = 2, x = y − 2, y = 2
Axis: x = −4
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
10) x = y3, x = 0, y = 1
Axis: x = −4
x
y
−8−6−4−2 2468
−8
−6
−4
−2
2
4
6
8
find more resources at oneclass.com
find more resources at oneclass.com
