Hello Angeezzzz,
We first should write the ellipse in standard form:
$$\frac{x^2}{60^2}+\frac{y^2}{50^2}=1$$
Thus, we see the length of the semi-major axis is 60. We may restrict ourselft to the first quadrant, and then by symmetry quadruple the result to get the total volume. The volume of an arbitrary rectangular slice is:
$$dV=bh\,dx$$
where:
$$b=y=\frac{\sqrt{3000^2-50^2x^2}}{60}$$
$$h=2y=\frac{\sqrt{3000^2-50^2x^2}}{30}$$
Hence, we may state:
$$dV=\frac{3000^2-50^2x^2}{1800}\,dx=-\frac{25}{18}\left(x^2-3600 \right)\,dx$$
And so the total volume is given by:
$$V=-\frac{50}{9}\int_0^{60}x^2-3600\,dx$$
Applying the FTOC, we obtain:
$$V=-\frac{50}{9}\left[\frac{x^3}{3}-3600x \right]_0^{60}=-\frac{50\cdot60^3}{9}\left(\frac{1}{3}-1 \right)=-\frac{50\cdot60^3}{9}\left(-\frac{2}{3} \right)=800000$$