The side of a square is 18 cm. which is 7.5 cm. more than radius of a circle. What is the area of the circle?

Options

A. `348.2cm^2`
B. `346.5cm6^2`.
C. `342.4cm^2`
D. `340.8cm^2`

Answer

To find the area of the circle given that the side of a square is 18 cm and is 7.5 cm more than the radius of the circle, we can follow these steps:

### Step 1: Find the radius of the circle
We know that the side of the square is 18 cm and it is 7.5 cm more than the radius of the circle. We can express this relationship mathematically as:

\[ \text{Side of square} = \text{Radius of circle} + 7.5 \]

Let \( r \) be the radius of the circle. Therefore, we can write:

\[ 18 = r + 7.5 \]

To find \( r \), we can rearrange the equation:

\[ r = 18 - 7.5 \]

Calculating this gives:

\[ r = 10.5 \, \text{cm} \]

### Step 2: Calculate the area of the circle
The area \( A \) of a circle is given by the formula:

\[ A = \pi r^2 \]

We will use \( \pi \approx \frac{22}{7} \) for our calculations. Substituting the radius \( r = 10.5 \, \text{cm} \) into the formula:

\[ A = \frac{22}{7} \times (10.5)^2 \]

Calculating \( (10.5)^2 \):

\[ (10.5)^2 = 110.25 \]

Now substituting back into the area formula:

\[ A = \frac{22}{7} \times 110.25 \]

### Step 3: Simplify the area calculation
To simplify the calculation, we can multiply:

\[ A = \frac{22 \times 110.25}{7} \]

Calculating \( 22 \times 110.25 \):

\[ 22 \times 110.25 = 2425.5 \]

Now divide by 7:

\[ A = \frac{2425.5}{7} \]

Calculating this gives:

\[ A = 346.5 \, \text{cm}^2 \]

### Final Answer
The area of the circle is \( 346.5 \, \text{cm}^2 \).

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