title: how to check if a solid rectangular box is a subset of solid ball
body: <p>Suppose we have been given the coordinates of the centre of a solid rectangular box, the box's length, breadth, height and a solid ball with a given centre and radius.  </p>
  
  <p>Is there a <strong><em>fast</em></strong> way to check if the box is a subset of the ball? The only simple method that comes to my mind is to check if each of the 8 corner vertices lies inside the sphere. If yes, the box is indeed a subset of the ball (by convexity property of the ball). </p>