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Question
The difference between the circumference and radius of a circle is 37 cm. The area of the circle is
Options
111 cm2
184 cm2
154 cm2
259 cm2
Solution
154 cm2
Let the radius be r cm.
We know:
Circumference of the circle = 2πr
Thus, we have:
2πr - r = 37
⇒ r (2π - 1) = 37
`⇒ "r" (2xx22/7-1) = 37`
`=> "r" (37/7) = 37`
`=> "r" = (37xx7/37)`
⇒ r = 7 cm
Radius = 7 cm
Now,
Area of the circle = πr2
`=(22/7xx7xx7) "cm"^2`
= 154 cm2
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