lgg23
  • lgg23
Find the volume of the solid obtained by rotating the region bounded by the given curve about the specified axis. x^2+(y-5)^2=16 about the y axis. Volume = __?__
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
so we have a donut pretty much
amistre64
  • amistre64
radius of 4; and we are 5 away from the center so yeah; a donut
amistre64
  • amistre64
shell method might be appicable

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amistre64
  • amistre64
|dw:1333341918298:dw|
amistre64
  • amistre64
\[\int 2pix\ f(x)\ dx\] \[f(x)=\sqrt{16-x^2}+5\] \[4pi\int_{2}^{10}x\sqrt{16-x^2}+5x\ dx\]
amistre64
  • amistre64
one idea that might work, and be simpler is this: |dw:1333342330845:dw|
amistre64
  • amistre64
we can still do shell method; but our radius is determined by 5+4cos(t) and our height is determined by 4sin(t) as t moves from 0 to pi \[2*2pi\int_{0}^{pi}(5+cos(t))(4sin(t))\ dt\] we double it to get the bottom of it as well
amistre64
  • amistre64
dropped a 4; should be 4 cos(t) in there

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