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When a circle has its radius increased by 1 cm, its area increases by 43 cm^2. To the nearest integer, how many centimeters was the radius of the circle before it was increased?

 Jul 28, 2022
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Let r be the original radius

 

We have that

 

New  area -  Old area =    43 cm^2

 

pi (r + 1)^2   -   pi r^2 =   43

 

pi ( r^2  + 2r + 1)  - pi r^2  = 43

 

r^2 + 2r + 1  - r^2  =   43 / pi

 

2r + 1  =  43/pi

 

2r  = 43/ pi  -  1

 

r =  (43/ pi - 1)   / 2  ≈     6 cm

 

 

cool cool cool

 Jul 28, 2022

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