The circumference of the circle whose area is 24.64 m^2 is:-

Options

A. a. 17.2cm
B. b. 17.4cm
C. c. 17.6cm
D. d. 18.0cm

Answer

To find the circumference of a circle whose area is given as 24.64 m², we can follow these steps:

### Step 1: Use the formula for the area of a circle.
The formula for the area \( A \) of a circle is:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle and \( \pi \) is approximately \( \frac{22}{7} \).

### Step 2: Set up the equation with the given area.
We know the area is 24.64 m², so we can set up the equation:
\[ 24.64 = \pi r^2 \]
Substituting the value of \( \pi \):
\[ 24.64 = \frac{22}{7} r^2 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), we can multiply both sides by \( \frac{7}{22} \):
\[ r^2 = 24.64 \times \frac{7}{22} \]

### Step 4: Calculate \( r^2 \).
Calculating the right-hand side:
\[ r^2 = 24.64 \times \frac{7}{22} = 24.64 \times 0.31818 \approx 7.84 \]

### Step 5: Find \( r \) by taking the square root of \( r^2 \).
Now, we take the square root of both sides to find \( r \):
\[ r = \sqrt{7.84} = 2.8 \, \text{m} \]

### Step 6: Use the radius to find the circumference.
The formula for the circumference \( C \) of a circle is:
\[ C = 2\pi r \]
Substituting the value of \( r \):
\[ C = 2 \times \frac{22}{7} \times 2.8 \]

### Step 7: Calculate the circumference.
First, we can simplify \( 2.8 \) by dividing it by \( 7 \):
\[ 2.8 \div 7 = 0.4 \]
Now substituting back:
\[ C = 2 \times 22 \times 0.4 = 17.6 \, \text{m} \]

### Final Answer:
The circumference of the circle is \( 17.6 \, \text{m} \).

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