Find the diameter of a circle whose circumference is 26.4 cm.

Options

A. 8.4 cm
B. 4.8 cm
C. 8 cm
D. 6 cm

Answer

To find the diameter of a circle whose circumference is 26.4 cm, we can follow these steps:

### Step 1: Understand the relationship between circumference and diameter
The circumference (C) of a circle is related to its diameter (D) by the formula:
\[ C = \pi D \]
We can also express this in terms of the radius (r):
\[ C = 2 \pi r \]

### Step 2: Use the given circumference to find the diameter
We know the circumference is given as 26.4 cm. We can rearrange the formula to solve for the diameter:
\[ D = \frac{C}{\pi} \]

### Step 3: Substitute the value of π
For practical calculations, we can use the approximation \( \pi \approx \frac{22}{7} \). Therefore, we can substitute this value into the formula:
\[ D = \frac{26.4}{\frac{22}{7}} \]

### Step 4: Simplify the expression
To simplify the division by a fraction, we multiply by its reciprocal:
\[ D = 26.4 \times \frac{7}{22} \]

### Step 5: Remove the decimal for easier calculation
To make calculations simpler, we can multiply both the numerator and the denominator by 10 to eliminate the decimal:
\[ D = \frac{264}{22} \times 7 \]

### Step 6: Perform the division
Now, divide 264 by 22:
\[ 264 \div 22 = 12 \]

### Step 7: Multiply by 7
Now multiply the result by 7:
\[ D = 12 \times 7 = 84 \]

### Step 8: Adjust for the factor we multiplied by
Since we multiplied by 10 earlier, we need to divide our final answer by 10:
\[ D = \frac{84}{10} = 8.4 \]

### Final Answer
Thus, the diameter of the circle is:
\[ \text{Diameter} = 8.4 \, \text{cm} \]

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