The difference between the circumference and the radius of a circle is 111 cm. The area of the circle is
Solution
Correct Answer: Option C
We know that, circumference of circle = 2πr
Where r = radius of circle
As per information given in problem,
∴ 2πr – r = 111
⇒ r (2π – 1) = 111
\(\begin{array}{l} \Rightarrow \;r\; = \;\frac{{111}}{{2\pi - 1\;}}\\ \Rightarrow \;r\; = \;\frac{{111}}{{2\; \times \;\frac{{22}}{7}\; - \;1\;}} = \;\frac{{111}}{{\;\frac{{44}}{7}\; - \;1\;}}\\ \Rightarrow \;r\; = \;\frac{{111 \times \;7\;}}{{\;37\;}} \end{array}\)
⇒ r = 21 cm
Now, area of circle, A = πr2
∴A = (22/7) × 21 × 21
⇒ A = 1386 cm2
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