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Question
The circumference of a circle exceeds its diameter by 450 cm. Find the area of the circle.
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Solution
Let the radius of a circle = r cm
⇒ Circumference of a circle = 2πr cm
Diameter of a circle = 2r cm
Now, Circumference of a circle - Diameter of a circle = 450m
⇒ 2πr - 2r = 450
⇒ 2r(π - 1) = 450
⇒ `2"r"(22/7 - 1)` = 450
⇒ `2"r" xx (15)/(7)` = 450
⇒ r = `(450 xx 7)/(2 xx 15)`
= 105cm
∴ Area of a circle
= πr2
= `(22)/(7) xx 105 xx 105`
= 34650cm2.
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