Final answer:
The volume of the ellipsoid x²+y²+4z²=100 is found by converting the equation into its standard form and using the ellipsoid volume formula, resulting in a volume of 2000/3 pi cubic units.
Step-by-step explanation:
To find the volume of the ellipsoid given by the equation x²+y²+4z²=100, we first need to rewrite the equation in its standard form x²/a² + y²/b² + z²/c² = 1, where a, b, and c are the semi-axes of the ellipsoid. In this case, by dividing both sides of the equation by 100, we can see that a=10, b=10, and c=5. The formula for the volume of an ellipsoid is V = 4/3 π a b c. Therefore, the volume V is V = 4/3 π (10) (10) (5), which simplifies to V = 2000/3 π cubic units.