Question

Find the radius of a circle whose circumference is
(i) 52.8 cm
(ii) 42 cm
(iii) 6.6 km

Answer 1

(i) We know that the circumference C of a circle of radius 'r' is given by:
C = 2$\mathrm{\pi }$r
$$\begin{gathered} \Rightarrow r=\frac{C}{2\mathrm{\pi }} \\ \mathrm{Here},C=52.8\mathrm{cm} \\ \Rightarrow r=\frac{52.8\times 7}{2\times 22}\mathrm{cm}=\frac{369.6}{44}\mathrm{cm}=8.4\mathrm{cm}. \end{gathered}$$.

​(ii) We know that the circumference C of a circle of radius 'r' is given by:
C = 2$\mathrm{\pi }$r
$$\begin{gathered} \Rightarrow r=\frac{C}{2\mathrm{\pi }} \\ \mathrm{Here},C=42\mathrm{cm} \\ \Rightarrow r=\frac{42\times 7}{2\times 22}\mathrm{cm}=\frac{294}{44}\mathrm{cm}=6.68\mathrm{cm}. \end{gathered}$$

(iii) We know that the circumference C of a circle of radius 'r' is given by:
C = 2$\mathrm{\pi }$r
$$\begin{gathered} \Rightarrow r=\frac{C}{2\mathrm{\pi }} \\ \mathrm{Here},C=6.6\mathrm{km} \\ \Rightarrow r=\frac{6.6\times 7}{2\times 22}\mathrm{km}=\frac{2.1}{2}\mathrm{km}=1.05\mathrm{km}. \end{gathered}$$