Harry_the_cat
Elite Member
- Joined
- Mar 16, 2016
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Would someone mind checking my solution please?
I am trying to find the volume of revolution generated by rotating the minor segment bounded by the line y=x and the circle with centre (1,2) and radius 1, about the line y=x.
What I did was rotate the whole thing 45 degrees clockwise about the origin and reduced the problem to a rotation about the x-axis. The new circle had centre \(\displaystyle (\frac{3}{\sqrt2}, \frac{1}{\sqrt2}) \)and x-intercepts \(\displaystyle \sqrt2\) and \(\displaystyle 2\sqrt2\).
The solution I got is 0.669 cubic units. Anyone like to check my give it a go and see if you get the same result?
Or is there another way to do it?
I am trying to find the volume of revolution generated by rotating the minor segment bounded by the line y=x and the circle with centre (1,2) and radius 1, about the line y=x.
What I did was rotate the whole thing 45 degrees clockwise about the origin and reduced the problem to a rotation about the x-axis. The new circle had centre \(\displaystyle (\frac{3}{\sqrt2}, \frac{1}{\sqrt2}) \)and x-intercepts \(\displaystyle \sqrt2\) and \(\displaystyle 2\sqrt2\).
The solution I got is 0.669 cubic units. Anyone like to check my give it a go and see if you get the same result?
Or is there another way to do it?