Find the radius and area of a circle, whose circumference is : 22 m

Answer

To find the radius and area of a circle whose circumference is 22 meters, we can follow these steps:

### Step 1: Write down the formula for the circumference of a circle.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the circle and \( \pi \) is approximately \( \frac{22}{7} \).

### Step 2: Set up the equation with the given circumference.
We know that the circumference is 22 meters, so we can set up the equation:
\[ 2 \pi r = 22 \]

### Step 3: Substitute the value of \( \pi \).
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 2 \times \frac{22}{7} \times r = 22 \]

### Step 4: Simplify the equation.
Now, simplify the left side:
\[ \frac{44}{7} r = 22 \]

### Step 5: Solve for \( r \).
To isolate \( r \), multiply both sides by \( \frac{7}{44} \):
\[ r = 22 \times \frac{7}{44} \]
\[ r = \frac{154}{44} = \frac{7}{2} \text{ meters} \]
This simplifies to:
\[ r = 3.5 \text{ meters} \]

### Step 6: Calculate the area of the circle.
Now that we have the radius, we can find the area \( A \) of the circle using the formula:
\[ A = \pi r^2 \]
Substituting \( \pi \) and \( r \):
\[ A = \frac{22}{7} \times \left(\frac{7}{2}\right)^2 \]

### Step 7: Simplify the area calculation.
Calculating \( \left(\frac{7}{2}\right)^2 \):
\[ \left(\frac{7}{2}\right)^2 = \frac{49}{4} \]
Now substituting back into the area formula:
\[ A = \frac{22}{7} \times \frac{49}{4} \]
\[ A = \frac{22 \times 49}{7 \times 4} \]

### Step 8: Perform the multiplication and division.
Calculating:
\[ A = \frac{1078}{28} \]
Now simplifying \( \frac{1078}{28} \):
\[ A = 38.5 \text{ square meters} \]

### Final Answers:
- Radius \( r = 3.5 \) meters
- Area \( A = 38.5 \) square meters

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