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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.”

User Kerberos
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1 Answer

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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
A manufacturer drills a round hole of radius r through the center of a metal sphere-example-1
User Oregano
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