- #1

skate_nerd

- 176

- 0

$$\frac{x^2}{16}+\frac{y^2}{9}+\frac{z^2}{1}=1$$

First, for each number t in the interval \(-1\leq{t}\leq{1}\) I need to find the area A(t) of the plane cross-section made by \(z=t\). This I know should be a function of \(t\).

After that I have to find the volume of this ellipsoid.

So far I have a sketch of this ellipsoid, which was pretty easy because it's just each denominator's square root is the length of the ellipsoid on that axis, respectively. However in my class so far we have only covered integrals and differentiation regarding vectors in 3-space. However to find an area, you need an integral, correct? I guess the bounds of the integral would probably be -1 to 1, but how would I go about finding a function to integrate? I'm assuming you would have to probably put this \(z=t\) in the ellipsoid's equation, but from there would I need to do something like solve for y? I guess I just need a little help getting started.