Question

Find the volume of the ellipsoid x^2+y^2+5z^2=64.

Answer 1

$x^2 +y^2+5z^2 = 64$

$\dfrac{x^2}{8^2} +\dfrac{y^2}{8^2} +\dfrac{z^2}{(\cfrac{8}{\sqrt5})^2} = 1\\ a = 8;\space b =8;\space c = {\cfrac{8}{\sqrt5}}\\ V =\cfrac{4}{3}\pi*a*b*c$

$V = \cfrac{4}{3}\pi*8*8*\dfrac{8}{\sqrt5} = \cfrac{512\sqrt5}{15}\pi =76.325\pi$