The Plane X + Y + Z = 1 Slices $\le$

The plane x + y + z = 1 slices the ball x² + y² + z² $\le$ 1 into two pieces. Find the volume of the smaller piece. (Hint: Replace the plane by a horizontal plane at the same distance from the origin.)

A) $\pi$ cubic units
B) $\pi$ cubic units
C) $\pi$ cubic units
D) $\pi$ cubic units
E) $\pi$ cubic units