Find the radius and circumference of a circle, whose area is : 154 `cm^(2)`

Answer

To find the radius and circumference of a circle whose area is given as 154 cm², we can follow these steps:

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

### Step 2: Set up the equation using the given area.
We know the area is 154 cm², so we can set up the equation:
\[ \pi r^2 = 154 \]

### Step 3: Substitute the value of \( \pi \).
Using \( \pi = \frac{22}{7} \), we substitute this into the equation:
\[ \frac{22}{7} r^2 = 154 \]

### Step 4: Multiply both sides by 7 to eliminate the fraction.
To simplify, multiply both sides by 7:
\[ 22 r^2 = 154 \times 7 \]
Calculating \( 154 \times 7 \):
\[ 154 \times 7 = 1078 \]
So, we have:
\[ 22 r^2 = 1078 \]

### Step 5: Divide both sides by 22.
Now, divide both sides by 22 to solve for \( r^2 \):
\[ r^2 = \frac{1078}{22} \]
Calculating \( \frac{1078}{22} \):
\[ r^2 = 49 \]

### Step 6: Take the square root of both sides to find \( r \).
Now, take the square root of both sides:
\[ r = \sqrt{49} = 7 \text{ cm} \]

### Step 7: Calculate the circumference of the circle.
Now that we have the radius, we can find the circumference \( C \) using the formula:
\[ C = 2 \pi r \]
Substituting the values:
\[ C = 2 \times \frac{22}{7} \times 7 \]
The \( 7 \) in the numerator and denominator cancels out:
\[ C = 2 \times 22 = 44 \text{ cm} \]

### Final Answers:
- Radius \( r = 7 \text{ cm} \)
- Circumference \( C = 44 \text{ cm} \)

---