[amp_mcq option1=”\[\frac{{4\pi {\rm{abc}}}}{{35}}\]” option2=”\[\frac{{{\rm{abc}}}}{{35}}\]” option3=”\[\frac{{2\pi {\rm{abc}}}}{{35}}\]” option4=”\[\frac{{\pi {\rm{abc}}}}{{35}}\]” correct=”option1″]
The correct answer is $\boxed{\frac{{\pi {\rm{abc}}}}{{35}}}$.
The surface $x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$ is an ellipsoid. The volume of an ellipsoid is given by the formula
$$V = \frac{4}{3} \pi abc \int_0^1 \int_0^1 \int_0^1 \sqrt{x^2/a^2 + y^2/b^2 + z^2/c^2} dx dy dz.$$
In this case, we have $x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$, so we can simplify the integral to
$$V = \frac{4}{3} \pi abc \int_0^1 \int_0^1 \int_0^1 \sqrt{1} dx dy dz = \frac{4}{3} \pi abc.$$
The other options are incorrect because they do not take into account the fact that the surface is an ellipsoid.