The length of a rectangle is 15 cm which is 6 cm less than the diameter of a circle. What is the area of the circle ?

Options

A. 346-5 sq cm
B. 173.25 sq cm
C. 156 sq cm
D. 132 sq cm

Answer

To solve the problem, we need to find the area of the circle given that the length of a rectangle is 15 cm and this length is 6 cm less than the diameter of the circle.

### Step-by-Step Solution:

1. **Identify the relationship between the rectangle's length and the circle's diameter.**
- The length of the rectangle is given as 15 cm, and it is stated that this length is 6 cm less than the diameter of the circle.
- We can express this relationship mathematically as:
\[ \text{Diameter of the circle} = \text{Length of the rectangle} + 6 \]

2. **Substitute the known value into the equation.**
- Substituting the length of the rectangle (15 cm) into the equation:
\[ \text{Diameter of the circle} = 15 + 6 = 21 \text{ cm} \]

3. **Calculate the radius of the circle.**
- The radius (r) of a circle is half of its diameter. Therefore:
\[ r = \frac{\text{Diameter}}{2} = \frac{21}{2} = 10.5 \text{ cm} \]

4. **Use the radius to find the area of the circle.**
- The area (A) of a circle is calculated using the formula:
\[ A = \pi r^2 \]
- Substituting the radius into the formula:
\[ A = \pi (10.5)^2 \]
- Calculating \( (10.5)^2 \):
\[ (10.5)^2 = 110.25 \]
- Thus, the area becomes:
\[ A = \pi \times 110.25 \]

5. **Approximate the area using the value of π.**
- Using \( \pi \approx 3.14 \):
\[ A \approx 3.14 \times 110.25 \approx 346.355 \]
- Rounding to two decimal places, the area of the circle is approximately:
\[ A \approx 346.36 \text{ cm}^2 \]

### Final Answer:
The area of the circle is approximately **346.36 cm²**.