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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?

 Jun 4, 2020
 #1
avatar+1130 
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since the circumfrence increases by 70% the diameter increses by 70% so we get the equation \(\frac{100}{17^2}\) which is \(\frac{100}{289}\)and you multiply it by 100 to get a percent so we get \(\frac{10000}{289}\) and appoxemetly \(34.6020761...\)

 Jun 4, 2020
 #2
avatar+21953 
0

Formula for the area of a circle:  Area  =  pi·diameter2/4

 

Old circumference = d   --->   old area  =  pi·d2/4

 

New circumference = 1.7d   --->   new area  =  pi·(1.7·d)2/4  =  2.89·pi·d2/4

 

To find the percentage increase, we first need to find the amount of increase:

                    amount of increase  =  new area - old area

                                                     =  2.89·pi·d2/4 - pi·d2/4

                                                     =  1.89·pi·d2/4

 

Now, we need to divide the amount of increase by the old area:

                  percentage increase  =  ( 1.89·pi·d2/4 ) / ( pi·d2/4 )

                                                     =  1.89

 

As a percentage:  189%  increase

 Jun 4, 2020

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