The correct answer is "452 in² " .
(assuming that the given value for the circumference is in "inches".
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Explanation:
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Area, "A" of a circle:
A = [tex] \pi [/tex] * r² ;
in which "r = the radius" .
We are given the Circumference, "C" of the circle:
C = 75.1 = 2 * [tex] \pi [/tex] * r ;
Using "3.14" for [tex] \pi [/tex] ;
Let us find the value for "r" (the radius"; so we can plug that value into the formula to find the area of the circle.
C = 2 * [tex] \pi [/tex] * r ;
→ 75.1 = 2 * 3.14 * r ;
Solve for "r" ;
→ 2 * 3.14 * r = 75.1 ;
Divide each side of the equation by: "(3.14 * 2)" ; to isolate "r" on one side of the equation; & to solve for "r" ;
→ [2 * 3.14 * r] / [2 * 3.14] = 75.1 / [2 * 3.14] ;
→ r = 75.1 / [2 * 3.14] ;
= 75.1 / (6.28) ;
= 11.9585987261146497 ; round to "12" ;
→ r = 12 ;
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To solve for the area of the circle:
Area, "A" = [tex] \pi [/tex] * r² ;
We are told to use: "3.14" for [tex] \pi [/tex] ; and we can substitute our calculate value of "12" for "r" ;
→ A = (3.14) * 12² ;
= (3.14) * 144 ;
= 452.16 ; round to the nearest square inch; assuming that the given values are in inches; we round to:
→ "452 in² " .
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