Finding Volume of Rugby Ball I am asked to find the volume of rugby ball whose surface is given by the ellipsoid:
$$\frac{x^2}{4} + \frac{y^2}{4} + \frac{z^2}{9} = 1$$
I am having trouble figuring out which coordinate system I should use. Is it possible to solve the triple integral of the volume by just using cartesian co-ordinates, without making conversions to the spherical or cylindrical coordinate system?   

Notice,
In general, the volume of ellipsoid $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ is $$=\frac{4\pi}{3}(abc)$$
Hence, the volume of ellipsoid $\frac{x^2}{4}+\frac{y^2}{4}+\frac{z^2}{9}=1\iff \frac{x^2}{2^2}+\frac{y^2}{2^2}+\frac{1^2}{3^2}=1$ is $$=\frac{4\pi}{3}(2\cdot2\cdot 3)$$  $$=\frac{48\pi}{3}$$ $$=\color{blue}{16\pi}$$
