In the equation of a circle the point $x$, $y$ lie on the circle because they satisfy the equation: $$x^2 + y^2 = r^2$$
Question: Similarly, is it possible to write equation for 3-dimensional objects that are lying in my surrounding?
These points should satisfy the equation so that these points form a 3-dimensional object.
Yes, a sphere:
$$ x^2 + y^2 + z^2 = r^2 $$