The area of a circle is `38.5 cm^(2)` . Find its diameter (in cm).

Options

A. 7
B. 14
C. 10
D. 20

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 the area \( A = 38.5 \, cm^2 \). Therefore, we can set up the equation:
\[ 38.5 = \pi r^2 \]

### Step 3: Use the value of \( \pi \).
For this calculation, we can use the approximate value of \( \pi \) as \( \frac{22}{7} \). Substituting this into the equation gives:
\[ 38.5 = \frac{22}{7} r^2 \]

### Step 4: Rearrange the equation to solve for \( r^2 \).
To isolate \( r^2 \), we can multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 38.5 \times \frac{7}{22} \]

### Step 5: Calculate \( r^2 \).
Calculating the right side:
\[ r^2 = 38.5 \times \frac{7}{22} = \frac{38.5 \times 7}{22} = \frac{269.5}{22} = 12.25 \]

### Step 6: Take the square root to find \( r \).
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{12.25} = 3.5 \, cm \]

### Step 7: Calculate the diameter.
The diameter \( d \) of the circle is twice the radius:
\[ d = 2r = 2 \times 3.5 = 7 \, cm \]

### Final Answer:
The diameter of the circle is \( 7 \, cm \).

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