When a circle has its radius increased by 1 cm, its area increases by 43 cm^2. To the nearest integer, how many centimeters was the radius of the circle before it was increased?
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When a circle has its radius increased by 1 cm, its area increases by 43 cm^2. To the nearest integer, how many centimeters was the radius of the circle before it was increased?
Area2 = Area1 + 43
Area1 = π r2
Area2 = π r2 + 43
Area2 = π (r + 1)2 ——> Area2 = Area2
π (r + 1)2 = π r2 + 43
divide both sides by π (r + 1)2 = r2 + 43
r2 + 2r + 1 = r2 + 43
subtract r2 from both sides 2r + 1 = 43
2r = 42
r = 21
check answer
π (21)2 + 43 =? π (22)2
(21)2 + 43 =? (22)2
441 + 43 =? 484
484 = 484 True
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