Find the diameter of a circle whose circumference is 63.8 m.

Options

A. 23.3m
B. 20.3m
C. 21.3m
D. 22.3m

Answer

To find the diameter of a circle whose circumference is 63.8 m, 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 and \( \pi \) is approximately \( \frac{22}{7} \).

### Step 2: Substitute the given circumference into the formula.
We know the circumference is 63.8 m, so we can set up the equation:
\[ 63.8 = 2 \pi r \]

### Step 3: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \), we substitute this into the equation:
\[ 63.8 = 2 \times \frac{22}{7} \times r \]

### Step 4: Simplify the equation.
First, we can multiply \( 2 \) and \( \frac{22}{7} \):
\[ 63.8 = \frac{44}{7} r \]

### Step 5: Isolate \( r \).
To find \( r \), we can multiply both sides by \( 7 \) to eliminate the fraction:
\[ 63.8 \times 7 = 44r \]
Calculating \( 63.8 \times 7 \):
\[ 446.6 = 44r \]

Now, divide both sides by \( 44 \):
\[ r = \frac{446.6}{44} \]

### Step 6: Calculate the radius.
Perform the division:
\[ r = 10.16 \, \text{m} \]

### Step 7: Find the diameter.
The diameter \( d \) is twice the radius:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 10.16 \]
Calculating this gives:
\[ d = 20.32 \, \text{m} \]

### Final Answer:
The diameter of the circle is approximately **20.32 m**.

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