Find the radius of a circular sheet whose area is `5544 m^(2)`

Answer

To find the radius of a circular sheet whose area is \( 5544 \, m^2 \), we can follow these steps:

### Step 1: Write 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: Set the area equal to the given value.
We know the area is \( 5544 \, m^2 \), so we can set up the equation:
\[ \pi r^2 = 5544 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), divide both sides by \( \pi \):
\[ r^2 = \frac{5544}{\pi} \]

### Step 4: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \), we substitute this value into the equation:
\[ r^2 = \frac{5544}{\frac{22}{7}} = 5544 \times \frac{7}{22} \]

### Step 5: Calculate \( 5544 \times 7 \).
First, multiply \( 5544 \) by \( 7 \):
\[ 5544 \times 7 = 38808 \]

### Step 6: Divide by \( 22 \).
Now, divide \( 38808 \) by \( 22 \):
\[ r^2 = \frac{38808}{22} \]

### Step 7: Perform the division.
Calculating \( 38808 \div 22 \):
\[ r^2 = 1764 \]

### Step 8: Find the radius \( r \).
To find \( r \), take the square root of \( 1764 \):
\[ r = \sqrt{1764} = 42 \, m \]

### Final Answer:
The radius of the circular sheet is \( 42 \, m \).

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