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The ratio of circumference and diameter of a circle is 22 : 7. If the circumference be $$1\frac{4}{7}$$ m, then the radius of the circle is :

The ratio of circumference and diameter of a circle is 22 : 7. If the circumference be $$1\frac{4}{7}$$ m, then the radius of the circle is : Correct Answer $$\frac{1}{4}\,m$$

Given :
$$\eqalign{ & \Rightarrow \frac{{{\text{Circumference of circle}}}}{{{\text{Diameter of circle }}}} = \frac{{22}}{7} \cr & \Rightarrow \frac{{{\text{Circumference of circle}}}}{{{\text{Twice of radius}}}} = \frac{{22}}{7} \cr & \Rightarrow \frac{{1\frac{4}{7}}}{{2r}} = \frac{{22}}{7} \cr & \Rightarrow \frac{{\frac{{11}}{7}}}{{2r}} = \frac{{22}}{7} \cr & \Rightarrow \frac{{11}}{{14r}} = \frac{{22}}{7} \cr & \Rightarrow 14r \times 22 = 11 \times 7 \cr & \Rightarrow r = \frac{{11 \times 7}}{{14 \times 22}} \cr & \Rightarrow r = \frac{1}{4}\,m \cr} $$

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