Seed5813
New member
- Joined
- Jan 29, 2018
- Messages
- 24
The region bound by
and the y axis is rotated about the line
A hole is drilled that takes up 1/4th the volume of the original volume, find the diameter to 3 decimal places.
2pi Int_0^8(8x - (x^3)/8)dx
... =256pi
Dividing by 4 yields 64pi
Code:
y=(1/8)x^2
Code:
y=8
A hole is drilled that takes up 1/4th the volume of the original volume, find the diameter to 3 decimal places.
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