find the volume of the solid generated by revolving about the y-axis the region bounded by x^2 + y^2 = a^2 , y = b>0 , x = 0

for b<=y<=a

(a spherical cap)

i assumed that y=b>0 meant to only count the graph above y=b

the answer i got was:

Pi * [ (a^4 -(a^6 / 3)) - ( (a^2)*b - (b^3 / 3) ) ]

sorry about all the brackets , i tried to make it as clean as possible

can someone check whether this is the correct answer and if not point me in the right direction