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+1
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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
+1130
+20

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
+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