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I have solved this question but I am trying it with another method. I am not getting the answer. Not sure where I am getting it wrong. Q. What will be the height along the surface of a paraboloid z=x^2+y^2(from z=0 to z=10) that will be equal to 1 units along the z-axis? First I calculated the volume using the triple Integral and then comparing it with the cylinder of similar cross-section I got the equivalent height for the bowl.

Another method which I am trying is to find the length of the parabolic curve z=y^2 from y=0 to y=1 but I am not getting the answer.

rku9
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  • The expression "What will be the height along the surface of ..." is unclear. Give some precision. – Jean Marie Nov 07 '16 at 08:00
  • The problem is to calibrate the bowl. So the length that has to be determined is identical to the length if the parabola z=y^2 from y=0 to y=1. Project the parabolic bowl in the y-z plane. The general length of the curve is the integral of (1+(f'(x))^2)^1/2 between the desired intervals. That is what I am doing. But not getting the answer. – rku9 Nov 08 '16 at 14:05

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An identical question is answered at Length of a Parabolic Curve

The answer there is quite detailed, so I didn't copy and paste it.

Community
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Steve B
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