I'm trying to calculate the volume of the hyperbola $\frac{x^{2}}{8.38^{2}}-\frac{y^{2}}{4.24^{2}}=1$ revolved around the y-axis with limits $\left\{-11.1\le y\le4.13\right\}$, and I'm attempting to use multiple methods. I first determined it with Cavalieri's principle, split up the created hyperboloid, integrated it from there, and got the value for volume as 2522.56. I attempted to solve it using double integrals, but I don't know where to start. Which variable should be integrated first?
2026-03-27 11:46:08.1774611968
Determining the volume of a hyperbola revolved around the y axis using double integrals
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