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

Options

A. 14 cm
B. 11 cm
C. 7 cm
D. 22 cm

Answer

To find the diameter of a circle when the area is given, we can follow these steps:

### Step-by-Step Solution:

1. **Write 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.

2. **Substitute the given area into the formula**:
We know the area \( A = 154 \, \text{cm}^2 \). Therefore, we can write:
\[ \pi r^2 = 154 \]

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

4. **Multiply both sides by 7 to eliminate the fraction**:
\[ 22 r^2 = 154 \times 7 \]
Calculate \( 154 \times 7 \):
\[ 154 \times 7 = 1078 \]
So, we have:
\[ 22 r^2 = 1078 \]

5. **Divide both sides by 22**:
\[ r^2 = \frac{1078}{22} \]
Calculate \( \frac{1078}{22} \):
\[ r^2 = 49 \]

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

7. **Calculate the diameter**:
The diameter \( d \) of a circle is twice the radius:
\[ d = 2r = 2 \times 7 = 14 \, \text{cm} \]

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

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