Answer: The circumference is: " 8.87 square units " . _________________________________________________ Explanation: _____________________________________ Note the following: ________________________________ Area of a circle: A = π r² = 25 units² ;
Circumference of a circle: C = π*d = 2πr ____________________________________ If we can solve for "r" ("radius", we can solve for the "Circumference, "C") ; __________________________________ A = π r² = 25 ;
C = 2 * π *r
So: " π * r * r = 25" ; ________________________ We know that: " π * r * r = 25" ;
Multiply EACH side of the equation by "2" ; __________________________________ 2*{ π * r * r = 25} ; __________________________________ 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 ; ______________________________ Divide EACH SIDE of the equation by "r" ; to isolate "C" on one side of the equation: ________________________________ (C * r) / r = 25 / r ;
to get: C = 25 / r ; ____________________________________ Now, we need to find the value for "r" (the radius); to find "C" (the circumference).
We know that: ____________________________________ π * r² = 25 ; ____________________________________ Divide each side of the equation by "π"; to isolate "r² " on one side of the equation; ____________________________________ (π * r²) / π = 25 / π ;
To get: ___________________________________________________ r² = 25/π ; Let us use "3.14" as an approximation for "π" ; ___________________________________________________ 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); _____________________________________________
+√(r²) = +√(7.9617834394904459) ; _____________________________________________ to get: _____________________________________________ r = 2.8216632399155016635 ; → Round to: " 2.82 " ; _____________________________________________ C = 25 / r ;
C = 25 / (2.82) = 8.8652482269503546 square units . → Round to: "8.87" square units. _____________________________________________ The answer is: "8.87 square units" . _____________________________________________
