Question

A manufacturer drills a round hole of radius r through the center of a metal sphere of radius r. find the volume of the remaining metal “bead.”

Answer 1

The media attached below is the bottom/top view of drilled sphere. If you look it from sideways, you'll see that the drilled hole is in the form of cylindrical shape. So,
Volume of the drilled shape= volume of cylinder = πr²h, where h is 2r.
∴Volume of cylinder(V1) = πr²(2r) = 2πr³.
Volume of sphere(V2) = 4πr³/3.

Therefore volume of remaining metal bead = V1 - V2
                                                                         =   2πr³ - 4πr³/3 
                                                                         =   (6πr³ - 4πr³)/3
                                                                         =   2πr³/3.

Hence volume of remaining bead is 2πr³/3