The region bound byand the y axis is rotated about the lineCode:y=(1/8)x^2A hole is drilled that takes up 1/4th the volume of the original volume, find the diameter to 3 decimal places.Code:y=8

2pi Int_0^8(8x - (x^3)/8)dx

... =256pi

Dividing by 4 yields 64pi

Code:64pi = 2pi Int_0^z(8x - (x^3)/8)dx 32 = Int_0^z(8x - (x^3)/8)dx 32 = 4b^2 - (b^4)/32 -(b^4)/32 + 4b^2 - 32 = 0 By quadratic formula: b^2 = (256 + 16sqrt(12)) and 256 - 16sqrt(12) Take three square root and multiply by 2, yielding Diameter = 35.295 or 28.325

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