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We define a solid A by: $$\frac{19}{x^2} + \frac{14}{y^2} \leq z^4 \quad (0 \leq z \leq 1)$$

We define a solid B by: $$x^2 + y^2 \leq z^4 \quad (0 \leq z \leq 1)$$

The volume of the solid B is ?

Please don't tell me the answer, just guide/tell me the things i need to know to solve the problem, i search on youtube "find volume from solid equation", but only got videos calculating known geometric figures.

ewokx
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Carlos
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  • Are you looking for the volume of $B$ in terms of the volume of $A,$ or on its own? If it's the former, then you'll likely want to look at how you can transform $B$ into $A$ or vice versa. If it's the latter, we'll likely need to do some integration. (which also doesn't seem so terrible if we use polar) – Stephen Donovan May 17 '22 at 00:40
  • I suppose that i'm looking for the volume of $B$ by its own, since the exercise above is an exact copy from the paper, with nothing else – Carlos May 17 '22 at 00:41
  • I'm not entirely sure to be honest, in that case I don't quite understand why we've defined $A.$ Anyway, are you familiar with multiple integration and cylindrical coordinates? – Stephen Donovan May 17 '22 at 00:46
  • I'm not familiar with it, but knowing that is a step further – Carlos May 17 '22 at 00:49
  • you can find an entire version of this problem here – Carlos May 17 '22 at 00:54

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