Cylindrical Shells Volume

  • Thread starter silverbell
  • Start date
  • #1

Homework Statement



Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis.

x= (y^2) +1

x= 0

y=1

y=2

Homework Equations



2∏ ∫ rh



The Attempt at a Solution



2∏ ∫ from 1 to 2 (y^2) + 1

I'm not sure where to go from here. :S Please help.
 

Answers and Replies

  • #2
35,439
7,308

Homework Statement



Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis.

x= (y^2) +1

x= 0

y=1

y=2

Homework Equations



2∏ ∫ rh



The Attempt at a Solution



2∏ ∫ from 1 to 2 (y^2) + 1

I'm not sure where to go from here. :S Please help.

Start with a sketch of the region that is being rotated. Then draw a sketch of the solid that is formed.
 
  • #3
I drew a sketch. I'm not sure what do do about the radius part. I know y= 2 is the higher radius along the x-axis. And y= 1 is the lower radius along the x-axis. Do I subtract the radius minus function?
 
  • #4
35,439
7,308
The expression for incremental volume (the volume of a thin horizontal strip that is revolved around the x-axis) is 2[itex]\pi[/itex] * radius * width of strip * Δy.

The radius varies from what to what?
How wide is a typical strip?
 

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