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The area of a circle is 1386 m^(2). Find...

 The area of a circle is `1386 m^(2)`. Find its circumference. 

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To find the circumference of a circle when the area is given, 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 from the problem that the area \( A \) is \( 1386 \, m^2 \). Therefore, we can write: \[ \pi r^2 = 1386 \] ### Step 3: Use the value of \( \pi \). For calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives: \[ \frac{22}{7} r^2 = 1386 \] ### Step 4: Solve for \( r^2 \). To isolate \( r^2 \), we can multiply both sides by \( 7 \) to eliminate the fraction: \[ 22 r^2 = 1386 \times 7 \] Calculating \( 1386 \times 7 \): \[ 1386 \times 7 = 9702 \] Thus, we have: \[ 22 r^2 = 9702 \] ### Step 5: Divide by 22 to find \( r^2 \). Now, we divide both sides by \( 22 \): \[ r^2 = \frac{9702}{22} \] Calculating \( \frac{9702}{22} \): \[ r^2 = 441 \] ### Step 6: Find the radius \( r \). To find \( r \), we take the square root of \( r^2 \): \[ r = \sqrt{441} = 21 \, m \] ### Step 7: 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 \( \pi \) and \( r \): \[ C = 2 \times \frac{22}{7} \times 21 \] ### Step 8: Simplify the expression. Calculating this step-by-step: 1. First, calculate \( 2 \times 22 = 44 \). 2. Then, \( 44 \times 21 = 924 \). 3. Finally, divide by \( 7 \): \[ C = \frac{924}{7} = 132 \, m \] ### Final Answer: The circumference of the circle is \( 132 \, m \). ---
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