What is the diameter of sphere with a surface area of 615.44 mm2? use 3.14 for π. a. 14 mm b. 12.56 mm c. 24.5 mm d. 7 mm

 The diameter of the circle is:  " 14 mm " .

Note:

The formula for the surface area is:

a = 4 * π * r² ;

in which:  "a = surface area of sphere. " ; 
                 π = 3.14; 
                 r = radius; 
                Note:  d = diameter = 2r  ;  r = radius = d/2 ; 

We want to find the diameter, "d" ;

Given:  a = 615.44 mm² .

 → a = 4 * π * r² ;

 → 615.44 mm²  = 4 * 3.14 * r² ; 

If we can solve for "r" (in "mm"); we can solve for "d" (diameter);

Note:  4 * 3.14  =  12.56 ; 

Rewrite as:

→  615.44 mm² = 12.56 * r² ;

Divide each side of the equation by "12.56" ; 

→ 615.44 mm² / (12.56) = (12.56 * r²) / 12.56 ; 

→ 49 mm² = r² ;

↔  r² = 49 mm²; 

Take the positive square root of EACH SIDE of the equation; 
  to isolate "r" on one side of the equation; & to solve for "r" (the "radius"); 

↔  √(r²) = √(49 mm²)  ;

to get: 

        r  =  7 mm ; 

Now, to find the diameter, "d" ; 

d = 2r = 2 * 7mm = 14 mm . 

 The diameter of the circle is:  " 14 mm " .

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