Answer: The diameter of the circle is: "200" .
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Note:
We are asked to find the "diameter, d" of a circle;
{with area, "A" , equal to: "31,416" } .
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Area of a circle, "A" :
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A = π r² ;
in which: "r" = radius ;
Let us use: "3.1416" for "π"
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The diameter, "d" :
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d = 2r ;
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We need to find "r" ; so we can find "d" ;
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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 ;
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We are asked to find the diameter, "d" ; of the circle:
d = 2 r ;
d = 2 (100) ;
d = 200 .
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The answer is: " 200 " .
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The diameter of the circle is: " 200 " .
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