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# Further Techniques for Integration watch

1. A circle has an equation x^2 +y^2=25 and the line y=4. A napkin ring is formed by rotating the shaded area through 360 degrees about the x-axis. By considering the shaded area as the difference between two area and hence the volume of the napkin ring as the difference between two volumes, find the volume of the napkin ring/
2. (Original post by CelaenSardothien)
A circle has an equation x^2 +y^2=25 and the line y=4. A napkin ring is formed by rotating the shaded area through 360 degrees about the x-axis. By considering the shaded area as the difference between two area and hence the volume of the napkin ring as the difference between two volumes, find the volume of the napkin ring/
Can u post the diagram and anything you have tried
3. Is this from A level Maths?
4. (Original post by thekidwhogames)
Is this from A level Maths?
yes
5. (Original post by CelaenSardothien)
yes
Make a drawing and let us know what you tried so we can help.
6. There's something missing from the text at the start of the question. Anyway, can you see that we're interested in the region between x = -3 and x = +3? That's where y = 4 intersects the circle. So the volume of the whole shape is pi * integral y^2 dx and the middle bit is just a cylinder radius 4, height 6. Subtract them and you're done.

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