The area of a circular tin plate is `38.5 m^(2)` . Find its circumference.

Options

A. 11 m
B. 22 m
C. 24 m
D. 41 m

Answer

To find the circumference of a circular tin plate given its area, we can follow these steps:

### Step 1: Understand 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 and \( \pi \) is a constant approximately equal to \( \frac{22}{7} \).

### Step 2: Substitute the given area into the formula.
We know the area of the circular tin plate is \( 38.5 \, m^2 \). Therefore, we can set up the equation:
\[ 38.5 = \pi r^2 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ 38.5 = \frac{22}{7} r^2 \]

### Step 3: Solve for \( r^2 \).
To isolate \( r^2 \), we first multiply both sides by \( 7 \) to eliminate the fraction:
\[ 38.5 \times 7 = 22 r^2 \]
Calculating \( 38.5 \times 7 \):
\[ 38.5 \times 7 = 269.5 \]
So we have:
\[ 269.5 = 22 r^2 \]
Next, divide both sides by \( 22 \):
\[ r^2 = \frac{269.5}{22} \]

### Step 4: Calculate \( r^2 \).
Now we perform the division:
\[ r^2 = \frac{269.5}{22} = 12.25 \]

### Step 5: Find the radius \( r \).
To find \( r \), we take the square root of \( r^2 \):
\[ r = \sqrt{12.25} = 3.5 \, m \]

### Step 6: Use the radius to find the circumference.
The formula for the circumference \( C \) of a circle is:
\[ C = 2 \pi r \]
Substituting \( r = 3.5 \, m \) and \( \pi = \frac{22}{7} \):
\[ C = 2 \times \frac{22}{7} \times 3.5 \]

### Step 7: Calculate the circumference.
First, simplify:
\[ C = 2 \times \frac{22 \times 3.5}{7} \]
Calculating \( 22 \times 3.5 = 77 \):
\[ C = 2 \times \frac{77}{7} \]
Now simplify \( \frac{77}{7} = 11 \):
\[ C = 2 \times 11 = 22 \, m \]

### Final Answer:
The circumference of the circular tin plate is \( 22 \, m \).

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