y = 3*sqrt(x) and y=6 intersect at x=4. So the limits of integration are from x=0 to x=4.
External radius r_ext(x) = 6, internal r_int = 3*sqrt(x).
So the volume ispi*int_from_0_to_4[r_ext^2(x) - r_int^2(x)]dx =
pi*int_from_0_to_4(36 - 9x)dx =9*pi*int_0_4(4 - x)dx =9pi*(4x - x^2/2)_0_4 =9pi*(16-0 - (4^2/2-0)) = 9pi*8 = 72pi.
thank you very much!!!
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