Question : The ratio of the circumference and diameter of a circle is $22: 7$. If the circumference is $1\frac{4}{7}$ m, then the radius of the circle is:
Option 1: $\frac{1}{3}$ m
Option 2: $\frac{1}{2}$ m
Option 3: $\frac{1}{4}$ m
Option 4: $1$ m
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Correct Answer: $\frac{1}{4}$ m
Solution :
Given: The ratio of the circumference and diameter of a circle is 22 : 7.
Its circumference is $1\frac{4}{7}$ m.
Let the radius of the circle be $r$ m.
So, diameter $=2r$ and its circumference is $2\pi r$.
According to the question,
$\frac{\text{Circumference}}{\text{Diameter}}=\frac{22}{7}$
⇒ $\frac{1\frac{4}{7}}{2r}=\frac{22}{7}$
⇒ $\frac{\frac{11}{7}}{2r}=\frac{22}{7}$
⇒ $\frac{11}{14r}=\frac{22}{7}$
$\therefore r=\frac{1}{4}$ m
Hence, the correct answer is $\frac{1}{4}$ m.
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