Question
Asked Oct 31, 2019
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For the solids of revolution, how do I know when to add or subtract from the axis of revolution such as when y=3, y=-2, or x=-2, x=2, for both disk, washer, and cylindrical shell method, when finding the volume?

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Expert Answer

Step 1

For the solids of revolution, find the volume using disk, washer and cylindrical shell method.

Step 2

a) Disk or Washer Method.

Take a cross-section perpendicular to axis of revolution. If the
cross-section is a solid disk, A = TR2. If the cross section is a
washer/ring/annulus, A = īR2 - nr
help_outline

Image Transcriptionclose

Take a cross-section perpendicular to axis of revolution. If the cross-section is a solid disk, A = TR2. If the cross section is a washer/ring/annulus, A = īR2 - nr

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Step 3

When the axis of revolution is horizont...

R= f(x)
R fx)
rgx)
= |[5(x)]2 dax
Tf()2g()]2 dx|
V =
a
R = fix)+
R= f(x) + e
= f(2) + c]2 - ne? dz
)- 9(2) + c]2 dz |
rc-fx
rc-fix)
R =c- gix)
b
b
b
e-g()[c- f(z)]2 dz|
Te2-Tcf()2 da
help_outline

Image Transcriptionclose

R= f(x) R fx) rgx) = |[5(x)]2 dax Tf()2g()]2 dx| V = a R = fix)+ R= f(x) + e = f(2) + c]2 - ne? dz )- 9(2) + c]2 dz | rc-fx rc-fix) R =c- gix) b b b e-g()[c- f(z)]2 dz| Te2-Tcf()2 da

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Math

Calculus