Finding the volume of an object with 3 parameters

I know how to find the volume of a sphere/ball around x-axis using:

$V=\pi {\int}_{a}^{b}{f}^{2}(x)dx$

Lets say if:

${x}^{2}+{y}^{2}={r}^{2}$

We do: $y=\sqrt{{r}^{2}-{x}^{2}}$

So now: $V=\pi {\int}_{-r}^{r}(\sqrt{{r}^{2}-{x}^{2}}{)}^{2}dx$

But the problem starts here:

Im given an equation of ellipsoid, it has 3 parameters:

${x}^{2}+4{y}^{2}+4{z}^{2}\le 4$

What do i do with the z parameter? How do i build y now? how does it fit to the equation by integrals of V?

I would like an explanation and not just a solution - because its homework.

I know how to find the volume of a sphere/ball around x-axis using:

$V=\pi {\int}_{a}^{b}{f}^{2}(x)dx$

Lets say if:

${x}^{2}+{y}^{2}={r}^{2}$

We do: $y=\sqrt{{r}^{2}-{x}^{2}}$

So now: $V=\pi {\int}_{-r}^{r}(\sqrt{{r}^{2}-{x}^{2}}{)}^{2}dx$

But the problem starts here:

Im given an equation of ellipsoid, it has 3 parameters:

${x}^{2}+4{y}^{2}+4{z}^{2}\le 4$

What do i do with the z parameter? How do i build y now? how does it fit to the equation by integrals of V?

I would like an explanation and not just a solution - because its homework.