SOLUTION: The radius of a grindstone diminishes as a result of use but its thickness remains unaltered. If its mass varies directly as the square of the radius when its thickness remains the

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Question 353821: The radius of a grindstone diminishes as a result of use but its thickness remains unaltered. If its mass varies directly as the square of the radius when its thickness remains the same, by how much must its radius diminish before half its mass is worn away?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Mass is directly related to volume.
Volume of a cylinder V1+=+pi%2Ar%5E2%2Ah where h is the thickness
V2 = V1/2
V2+=+pi%2Ar%5E2%2Ah%2F2
r+=+sqrt%28V%2F%282pi%2Ah%29%29
--> the radius decreasing by a factor of sqrt(2) reduces the volume and mass by 1/2.
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This solution is simplistic because it ignores the hole in the wheel used to mount it. That can be calculated too, but I doubt it's expected.