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Volume using the disk method

  • #1

Homework Statement


Use the functions:
y=x+1, y=0, x=0, x=2

Find the volume when rotated around y=3
Find the volume when rotated around y=-1

Homework Equations


PI[tex]\int[/tex] R2dx or perhaps PI[tex]\int[/tex] R2 - r2dx

The Attempt at a Solution



i don't think that this is a particularly hard question, but I just can't seem to get the right answer. (perhaps I'm making a silly mistake)

So first I graphed the equations, all in the first quadrant, vertical line at x=2. bounded region looks like a trapezoid.

attempt:
PI[tex]\int[/tex] (from 0-2) of [3-(x+1)]2 dx

however the answer is 46pi/3 and I get 8pi/3 <-- very obviously wrong.
is this a washer method problem?

for the next, PI[tex]\int[/tex] (from 0-2) of [1+(x+1)]2 dx

i get 32pi/3 and the answer is 50pi/3


thanks :)
 

Answers and Replies

  • #2
33,153
4,838

Homework Statement


Use the functions:
y=x+1, y=0, x=0, x=2

Find the volume when rotated around y=3
Find the volume when rotated around y=-1

Homework Equations


PI[tex]\int[/tex] R2dx or perhaps PI[tex]\int[/tex] R2 - r2dx
It's the second one.

The Attempt at a Solution



i don't think that this is a particularly hard question, but I just can't seem to get the right answer. (perhaps I'm making a silly mistake)

So first I graphed the equations, all in the first quadrant, vertical line at x=2. bounded region looks like a trapezoid.

attempt:
PI[tex]\int[/tex] (from 0-2) of [3-(x+1)]2 dx
The volume of your typical volume element is [itex]\Delta V = \pi (R^2 - r^2) \Delta x[/itex]. It's not [itex]\Delta V = \pi (R - r)^2 \Delta x[/itex]. Do you see what you're doing wrong?
however the answer is 46pi/3 and I get 8pi/3 <-- very obviously wrong.
is this a washer method problem?

for the next, PI[tex]\int[/tex] (from 0-2) of [1+(x+1)]2 dx

i get 32pi/3 and the answer is 50pi/3


thanks :)
 

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