The ratio of circumference nd diameter of a circle is 22 : 7. If the circumference be `1(4)/(7)m`, then the radius of the circle is :

Options

A. `(1)/(3)m`
B. `(1)/(2)m`
C. `(1)/(4)m`
D. 1m

Answer

To solve the problem step by step, we will use the given information about the circumference and the ratio of circumference to diameter.

### Step 1: Understand the relationship between circumference and diameter
The ratio of the circumference (C) to the diameter (D) of a circle is given as 22:7. This means:
\[ \frac{C}{D} = \frac{22}{7} \]

### Step 2: Express the circumference in terms of diameter
From the ratio, we can express the circumference as:
\[ C = \frac{22}{7} \times D \]

### Step 3: Convert the given circumference to an improper fraction
The circumference is given as \( 1 \frac{4}{7} \) meters. We convert this mixed number to an improper fraction:
\[ 1 \frac{4}{7} = \frac{7 \times 1 + 4}{7} = \frac{11}{7} \text{ meters} \]

### Step 4: Set up the equation using the circumference
Now, we can set up the equation using the value of the circumference:
\[ \frac{11}{7} = \frac{22}{7} \times D \]

### Step 5: Solve for the diameter
To find the diameter (D), we can rearrange the equation:
\[ D = \frac{11}{7} \div \frac{22}{7} = \frac{11}{7} \times \frac{7}{22} = \frac{11}{22} = \frac{1}{2} \text{ meters} \]

### Step 6: Find the radius
The diameter (D) is twice the radius (r):
\[ D = 2r \]
So, we can find the radius:
\[ r = \frac{D}{2} = \frac{1/2}{2} = \frac{1}{4} \text{ meters} \]

### Final Answer
The radius of the circle is \( \frac{1}{4} \) meters.

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