Find the volume of the solid generated by revolving the foll

Find the volume of the solid generated by revolving the following region about the y-axis. The region in the first quadrant bounded above by the parabola y = 2x^2, below by the x-axis, and on the right by the line X =2.

Solution

Volume = pix^2 dy

Y =2x^2

x^2 =y/2

And at x=2 , y =8

so V = pi*x^2 dy = pi*y/2 dy from y=0 to 8

V = pi/4*y^2 ] from y=0 to 8

V = 16 pi = 50.24 unit (Ans)