how do i find the volume revolving around y=2 with the line y=2 and y=2sinx between 0 and pi/2

how do i find the volume revolving around y=2 with the line y=2 and y=2sinx between 0 and pi/2

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i figured it out...but i dont know why it must be calculated that way

for those who want to know what i got:
int(pi(2-2sinx)^2dx,x,0,pi/2)= pi(3pi-8)

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