The area of a circle is 154 `cm^2`. Its diameter is

Options

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Answer

To find the diameter of a circle given its area, 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 of the circle.

### Step 2: Substitute the given area into the formula.
We know that the area of the circle is \( 154 \, \text{cm}^2 \). Therefore, we can write:
\[ \pi R^2 = 154 \]

### Step 3: Use the value of \( \pi \).
For our calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ \frac{22}{7} R^2 = 154 \]

### Step 4: Solve for \( R^2 \).
To isolate \( R^2 \), multiply both sides by \( \frac{7}{22} \):
\[ R^2 = 154 \times \frac{7}{22} \]

### Step 5: Simplify the right side.
First, divide \( 154 \) by \( 22 \):
\[ 154 \div 22 = 7 \]
Now substitute back:
\[ R^2 = 7 \times 7 \]
So,
\[ R^2 = 49 \]

### Step 6: Find the radius \( R \).
Taking the square root of both sides gives:
\[ R = \sqrt{49} = 7 \, \text{cm} \]

### Step 7: Calculate the diameter.
The diameter \( D \) of the circle is twice the radius:
\[ D = 2R = 2 \times 7 \, \text{cm} = 14 \, \text{cm} \]

### Final Answer:
The diameter of the circle is \( 14 \, \text{cm} \).

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