Plane and sphere

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One group member will plot a plane intersecting a sphere.

One group member will produce a plot like this one:

This is the intersection of a sphere of radius $4$ centered at the origin with the plane $x=3$ .

You need to reproduce this plot along with a circle at the intersection. As a gesture of friendship, I will tell you that the parametric formula for a sphere of radius $R$ is:

$\begin{align*} x(s,t) &= R\cdot \cos(t)\sin(s)\\ y(s,t) &= R\cdot \sin(t)\sin(s)\\ z(s,t) &= R\cdot \cos(s), \end{align*}$

where $0\le t< 2\pi$ and $0\le s \le \pi$ .

You may make the circle indicating the intersection of any color you wish.