Question

The difference between the circumference and radius of a circle is 37cm. Using $\mathrm{\pi }=\frac{22}{7}$ , find the circumference of the circle. [CBSE 2013]

Answer 1

Let the radius of the circle be r and circumference C.
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Now,
$$\begin{gathered} C-r=37 \\ \Rightarrow 2\mathrm{\pi }r-r=37 \\ \Rightarrow r\left(2\times \frac{22}{7}-1\right)=37 \\ \Rightarrow r=\frac{37\times 7}{37}=7\mathrm{cm} \end{gathered}$$
Now, $C=2\mathrm{\pi }r=2\times \frac{22}{7}\times 7=44\mathrm{cm}$
Hence, the circumference of the circle is 44 cm.