How do you make a player die after time runs out?

You could use this:
WorldRoot:GetPartBoundsInBox (roblox.com)
And make its size the same as your sphere, althought the hitbox would be a cube, or you could also use ZonePlus v3.2.0 | Construct dynamic zones and effectively determine players and parts within their boundaries - Resources / Community Resources - DevForum | Roblox