What’s the diameter of a circle if the area is 31,416

 The diameter of the circle is:  "200" .


Note:  

We are asked to find the "diameter, d" of a circle;
{with area, "A" , equal to:  "31,416" } .

Area of a circle, "A" :

A = π r² ;

in which:  "r" = radius ; 

Let us use:  "3.1416" for "π"

The diameter,  "d" :

    d = 2r ;


We need to find "r" ; so we can find "d" ;

Given:  A = 31,416 ;

A = π r² ;

31,416 = (3.1416) * (r²) ;

↔  (3.1416) * (r²) = 31,416 ;

Divide each side of the equation by:  "(3.1416)" ; 

    [(3.1416) * (r²) ] / (3.1416) = (31,416) / (3.1416) ;

to get: 

              r²  =  10,000

           Now, take the "positive" square root of EACH SIDE of the equation; to isolate "r" on one side of the equation; & to solve for "r" ;

           √(r²) = √(10,000) ;

              r  =  100 ;

We are asked to find the diameter, "d" ; of the circle:

              d = 2 r ;

              d = 2 (100) ;

              d = 200 .

The answer is:  " 200 " .    

The diameter of the circle is:  " 200 " .