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The area of a circle is halves when x meters is subtracted from its radius.  If the original circle has a radius of 40 m, what is the value of x?  Round your answer to the nearest tenth.

 Mar 30, 2021
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Area  of original circle =  pi * 40^2  =  1600pi  m^2

 

1/2 of this  = 800 pi  m^2

 

So

 

800 pi =  pi ( 40 - x)^2

 

800 = (40 - x)^2              take the positive root

 

sqrt (800)  =  40 - x              simplify

 

20sqrt (2)  =  40 - x           rearrange  as

 

x  = 40  - 20sqrt (2)   =  20  [  2 - sqrt (2) ]  m  ≈  11.7  m

 

 

cool cool cool

 Mar 30, 2021

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