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Aneli [31]
3 years ago
8

A manufacturer drills a round hole of radius r through the center of a metal sphere of radius r. find the volume of the remainin

g metal “bead.”

Mathematics
1 answer:
Kisachek [45]3 years ago
3 0
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
                                                                         =   2
πr³ - 4πr³/3 
                                                                         =   (6πr³ - 4πr³)/3
                                                                         =   2
πr³/3.

Hence volume of remaining bead is 2
πr³/3

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