Posted by **Laurie** on Thursday, July 19, 2012 at 6:47pm.

find the volume of the solid generated by revolving the region r bounded by the graphs of the given equations about the y-axis.

x^2+y^2=1

x=1

y=1

- Calculus Voulme -
**Reiny**, Thursday, July 19, 2012 at 9:57pm
I see a cylinder of radius 1 and height 1, containing a half sphere.

so volume of your generated solid

= π(1^1)(1) - (1/2)(4/3)π(1^3)

= π - (2/3)π

= π/3

- Calculus Voulme -
**Reiny**, Thursday, July 19, 2012 at 10:18pm
same question by Calculus

using "washers"

outer radius = r1 = 1 --->r1^2 = 1

inner radius = r2 = √(1-y^2) --->r2^2 = 1-y^2

Volume = π∫(1 - (1-y^2) dy from y = 0 to 1

= π∫y^2 dy from y = 0 to 1

= π[ y^3/3] from 0 to 1

= π(1/3 - 0) = π/3 , same as above

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