Calculus
posted by Anonymous .
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations y = 0.5x^2, y = 2, and x = 0 about the line y = 2.
A. 8pi/15
B. 32pi/15
C. 64pi/15
D. 4pi/15
E. 16pi/15

v = ∫ πr^2 dx
where r=2y
v = ∫[0,2] π(2x^2/2)^2 dx
or
v = ∫ 2πrh dy
where r=2y and h=x
v = ∫[0,2] 2π(2y)√(2y) dy 
How do you know the r is 2y and not just y?

Because it is rotated about the line y = 2 ,
not y = 0 , which would have been the xaxis
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