SOLUTION: The radius of a grindstone diminishes as a result of frequent use, but its thickness remains unaltered. If its mass is directly proportional to the square of the radius when its th

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Question 1176610: The radius of a grindstone diminishes as a result of frequent use, but its thickness remains unaltered. If its mass is directly proportional to the square of the radius when its thickness remains the same, by how much must its radius decreases before half of its mass is worn away
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
M=kr^2
0.5M=k(r1^2)
M=2k(r1^2)
so 2kr1^2=kr^2
2 r1^2=r^2
1/2=r1^2/r^2
sqrt(2)/2=r1/r2
it will decrease by 1-sqrt(2)/2 or (2-sqrt(2))/2
or about 29.3%
sqrt(2)=0.7071, which is the ratio of the smaller to the larger.