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 yaxis.
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 = √(1y^2) >r2^2 = 1y^2
Volume = π∫(1  (1y^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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