If it was a 6 inch high cylinder you might have better luck. You would still have to successfully argue that nothing constitutes a 6 inch hole with infinitly thin sides. As it is a sphere if the drill is the same size as the sphere the hole at the end of drilling is 0 inches (the drill bit may have traveled 6 inches or more but we are measuring the hole not drill travelling). The depth of the hole (or height of the resulting doughnut) changes when you drill through the sphere as the drill knocks off the top and bottom of the sphere.
Although we are not told the width of the sphere or the width of the drill the width of sphere and drill are related. With a sphere with a 6 inch diameter the drill must be 0 inches wide, with a 60 inch diameter sphere the drill will need to be about 59.7 inches (the drill will travel 60 inches, but the remaining hole will be 6 inches)