Given the ellipsoid [tex]x^2+y^2+4z^2=100[/tex]
For the radius in the x-dirextion, y = z = 0, and we have
[tex]x^2=100 \\ \\ \Rightarrow x=\pm10[/tex]
For the radius in the y-dirextion, x = z = 0, and we have
[tex]y^2=100 \\ \\ \Rightarrow y=\pm10[/tex]
For the radius in the z-dirextion, x = y = 0, and we have
[tex]4z^2=100 \\ \\ \Rightarrow z^2=25 \\ \\ \Rightarrow z=\pm5[/tex]
Thus, the radius of the ellipsoid is given by
[tex]Volume=4\pi r^3=4\pi\times10\times10\times5=500\pi[/tex]
