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.

Question

A. 8pi/15
B. 32pi/15
C. 64pi/15
D. 4pi/15
E. 16pi/15

Answer 1

v = ∫ πr^2 dx
where r=2-y
v = ∫[0,2] π(2-x^2/2)^2 dx

or

v = ∫ 2πrh dy
where r=2-y and h=x
v = ∫[0,2] 2π(2-y)√(2y) dy

Answer 2

How do you know the r is 2-y and not just y?

Answer 3

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