Question

What is the circumference of a circle with an area of 25??

Answer 1

Answer:  The circumference is:  " 8.87 square units " .
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Explanation:
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Note the following:
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Area of a circle:  A = π r² = 25 units² ; 
 
Circumference of a circle:  C = π*d = 2πr
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  If we can solve for "r" ("radius", we can solve for the "Circumference, "C") ;
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   A = π r² = 25 ;

    C = 2 * π *r
 
   So:  " π * r * r = 25"  ;
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 We know that:  " π * r * r = 25" ; 

Multiply EACH side of the equation by "2" ; 
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      2*{ π * r * r = 25} ;
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To get:  2 * π * r * r = 25 ; 

Note:  "C = 2* π * r ; 

So,  "(2 * π * r) * r = 25 " ; 

We want to solve for "C" ; so replace the "(2 * π * r) " ; with "C" ;
 
          C * r = 25 ; 
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Divide EACH SIDE of the equation by "r" ; to isolate "C" on one side of the equation:
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   (C * r) / r  =  25 / r   ;

to get:    C  =  25 / r ;  
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Now, we need to find the value for "r" (the radius);
          to find "C" (the circumference).

We know that:  
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   π * r² = 25 ;
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Divide each side of the equation by "π"; to isolate "r² " on one side of the equation;
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   (π * r²) / π  =  25 / π ;

To get:  
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   r²  =  25/π  ;  Let us use "3.14" as an approximation for "π" ;
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   r²  =  25 / (3.14) ; 
  
   r²  =  7.9617834394904459 ; 

Take the "positive" square root of EACH side of the equation; 
   (since the radius, "r", cannot be a negative value);
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   +√(r²) = +√(7.9617834394904459) ; 
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to get:
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      r  =  2.8216632399155016635 ;  
              →  Round to:  " 2.82 " ; 
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     C = 25 / r  ;
 
     C = 25 / (2.82) = 8.8652482269503546  square units .
                              →  Round to:  "8.87"  square units.
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The answer is:  "8.87 square units" .
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