Find the radius and area of a circle, whose circumference is : 132 cm

Answer

To find the radius and area of a circle whose circumference is 132 cm, 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.

### Step 2: Substitute the given circumference into the formula.
We know that the circumference is 132 cm, so we can set up the equation:
\[ 2 \pi r = 132 \]

### Step 3: Solve for the radius (r).
To isolate \( r \), we can rearrange the equation:
\[ r = \frac{132}{2 \pi} \]
Using \( \pi \approx \frac{22}{7} \), we can substitute this value into the equation:
\[ r = \frac{132}{2 \times \frac{22}{7}} \]

### Step 4: Simplify the expression.
Calculating the denominator:
\[ 2 \times \frac{22}{7} = \frac{44}{7} \]
Now substituting back into the equation for \( r \):
\[ r = \frac{132 \times 7}{44} \]

### Step 5: Calculate the radius.
Now we simplify:
\[ r = \frac{924}{44} = 21 \text{ cm} \]
So, the radius of the circle is 21 cm.

### Step 6: Find the area of the circle.
The formula for the area (A) of a circle is given by:
\[ A = \pi r^2 \]
Substituting \( r = 21 \) cm into the area formula:
\[ A = \pi (21)^2 \]
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 441 \]

### Step 7: Calculate the area.
Now we simplify:
\[ A = \frac{22 \times 441}{7} = \frac{9702}{7} = 1386 \text{ cm}^2 \]
So, the area of the circle is 1386 cm².

### Final Answer:
- Radius: 21 cm
- Area: 1386 cm²

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