The side of a square is 5 cm which is 13 cm less than the diameter of a circle. What is the approximate area of the circle?

Options

A. 245 sq cm
B. 235 sq cm
C. 265 sq cm
D. 255 sq cm

Answer

To solve the problem step-by-step, we can follow these instructions:

### Step 1: Understand the relationship between the square and the circle
The problem states that the side of a square is 5 cm, which is 13 cm less than the diameter of a circle.

### Step 2: Calculate the diameter of the circle
We can express the diameter of the circle in terms of the side of the square:
\[ \text{Diameter of the circle} = \text{Side of the square} + 13 \text{ cm} \]
Substituting the value of the side of the square:
\[ \text{Diameter of the circle} = 5 \text{ cm} + 13 \text{ cm} = 18 \text{ cm} \]

### Step 3: Calculate the radius of the circle
The radius is half of the diameter:
\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{18 \text{ cm}}{2} = 9 \text{ cm} \]

### Step 4: Use the formula for the area of a circle
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the value of \( r \):
\[ A = \pi (9 \text{ cm})^2 \]

### Step 5: Substitute the value of \( \pi \)
Using \( \pi \approx \frac{22}{7} \):
\[ A = \frac{22}{7} \times 81 \text{ cm}^2 \]

### Step 6: Calculate the area
Now, we can calculate:
\[ A = \frac{22 \times 81}{7} = \frac{1782}{7} \approx 254.57 \text{ cm}^2 \]

### Step 7: Round the area to the nearest whole number
The approximate area of the circle is:
\[ A \approx 255 \text{ cm}^2 \]

### Final Answer
The approximate area of the circle is **255 cm²**.

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