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The diameter of a circle is increased so that the circumference increases by 70%. By what percent does the area increase?

Guest Nov 6, 2017
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If the circumference - a linear measure -  increases by 70%..it is now 1.7 times as large........the diameter and the radius which are also linear measures will also be 1.7 times as large.....so this is the scale factor

 

So......the new area will increase by the square of this scale factor  = (1.7)^2  = 2.89 times = 189%

 

[ To see this....note that if it doubles....it increases by 100%....and if it triples, it increases by 200%

 

So.....2.89 times must lie between 100% and 200% ]

 

 

 

cool cool cool

CPhill  Nov 6, 2017

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