Question

Find the volume of the ellipsoid x2+y2+4z2=100x2+y2+4z2=100.

Answer 1

Given the ellipsoid $x^2+y^2+4z^2=100$

For the radius in the x-dirextion, y = z = 0, and we have

$x^2=100 \\ \\ \Rightarrow x=\pm10$

For the radius in the y-dirextion, x = z = 0, and we have

$y^2=100 \\ \\ \Rightarrow y=\pm10$

For the radius in the z-dirextion, x = y = 0, and we have

$4z^2=100 \\ \\ \Rightarrow z^2=25 \\ \\ \Rightarrow z=\pm5$

Thus, the radius of the ellipsoid is given by

$Volume=4\pi r^3=4\pi\times10\times10\times5=500\pi$