If the circumference of a circle is 88 cm, what must be its area (in `cm^(2)`) ?

Options

A. 1232
B. 616
C. 704
D. 1408

Answer

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

### Step 1: Write down the formula for the circumference of a circle.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given circumference into the formula.
We know from the problem that the circumference \( C \) is 88 cm. Therefore, we can set up the equation:
\[ 2\pi r = 88 \]

### Step 3: Solve for the radius \( r \).
First, we can isolate \( r \) by dividing both sides by \( 2\pi \):
\[ r = \frac{88}{2\pi} \]
Now substituting \( \pi \) with \( \frac{22}{7} \):
\[ r = \frac{88}{2 \times \frac{22}{7}} = \frac{88 \times 7}{44} = \frac{616}{44} = 14 \text{ cm} \]

### Step 4: Write down the formula for the area of a circle.
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]

### Step 5: Substitute the radius into the area formula.
Now that we have \( r = 14 \) cm, we can substitute this value into the area formula:
\[ A = \pi (14)^2 \]
Substituting \( \pi \) with \( \frac{22}{7} \):
\[ A = \frac{22}{7} \times 14^2 = \frac{22}{7} \times 196 \]

### Step 6: Simplify the area calculation.
Calculating \( 14^2 \):
\[ 14^2 = 196 \]
Now substituting back:
\[ A = \frac{22 \times 196}{7} \]
Calculating \( \frac{196}{7} = 28 \):
\[ A = 22 \times 28 \]
Now calculate \( 22 \times 28 \):
\[ A = 616 \text{ cm}^2 \]

### Final Answer:
The area of the circle is \( 616 \text{ cm}^2 \).

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