I assume the volume you are trying to find is the set (where ).

The Jacobian theorem says,

Here is a differenciable vector function.

And is the determinant of the Frechet' derivative i.e. the Jacobian.

Of course, is the set

It is conventient to have be such a function so that .

If we let then .

Thus, .

This means, the function (thinking of vectors in as coloums).

Now, this is convenient because

The volume of is given by,

But,

Thus the volume is because the volume of a sphere is