# Calculus Voulme

posted by Laurie

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

1. Reiny

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

2. Reiny

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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