- Circle $$ A $$ has a diameter of approximately 20 inches and an area of approximately 300 inches squared. Which of these could be the area of Circle $$ B $$ ? A. About 100 inches squared B. About 300 inches squared C. About 900 inches squared D. About 2700 inches squared

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To determine the area of Circle $$ B $$, we first need to confirm the area of Circle $$ A $$ and its relationship to its diameter.

1. **Calculate the radius of Circle $$ A $$**:
   The diameter of Circle $$ A $$ is approximately 20 inches, so the radius $$ r $$ is:
   $$
   r = \frac{\text{diameter}}{2} = \frac{20}{2} = 10 \text{ inches}
   $$

2. **Calculate the area of Circle $$ A $$**:
   The area $$ A $$ of a circle is given by the formula:
   $$
   A = \pi r^2
   $$
   Substituting the radius:
   $$
   A = \pi (10)^2 = 100\pi \text{ square inches}
   $$
   Approximating $$ \pi $$ as 3.14, we find:
   $$
   A \approx 100 \times 3.14 = 314 \text{ square inches}
   $$
   This is close to the given area of approximately 300 square inches, confirming our calculations.

3. **Determine the possible areas for Circle $$ B $$**:
   The area of Circle $$ B $$ could be related to Circle $$ A $$ in various ways. The options provided are:
   - A. About 100 inches squared
   - B. About 300 inches squared
   - C. About 900 inches squared
   - D. About 2700 inches squared

We can analyze these options based on the relationship between the areas of circles. The area of a circle scales with the square of the radius.

- If Circle $$ B $$ has a radius that is half of Circle $$ A $$ (5 inches), its area would be:
     $$
     A_B = \pi (5)^2 = 25\pi \approx 78.5 \text{ square inches} \quad (\text{not an option})
     $$
   - If Circle $$ B $$ has the same radius as Circle $$ A $$ (10 inches), its area would be approximately 300 square inches (option B).
   - If Circle $$ B $$ has a radius that is 1.5 times that of Circle $$ A $$ (15 inches), its area would be:
     $$
     A_B = \pi (15)^2 = 225\pi \approx 706.5 \text{ square inches} \quad (\text{not an option})
     $$
   - If Circle $$ B $$ has a radius that is 3 times that of Circle $$ A $$ (30 inches), its area would be:
     $$
     A_B = \pi (30)^2 = 900\pi \approx 2827.4 \text{ square inches} \quad (\text{close to option D})
     $$

4. **Conclusion**:
   The areas of Circle $$ B $$ could reasonably be:
   - About 300 inches squared (same as Circle $$ A $$)
   - About 900 inches squared (if the radius is 30 inches)
   - About 2700 inches squared (if the radius is 30 inches, but this is a bit larger than the calculated area)

Thus, the most reasonable options for the area of Circle $$ B $$ are:
- B. About 300 inches squared
- C. About 900 inches squared

Since the question asks for which of these could be the area of Circle $$ B $$, the answer is:

**B. About 300 inches squared** and **C. About 900 inches squared**.

However, if we must choose only one option, the best answer is:

**C. About 900 inches squared**.
The area of Circle $$ B $$ could be about 300 or 900 square inches. The best answer is C. About 900 inches squared.

Circle has a diameter of approximately 20 inches and an area of approximately 300 inches squared.
Which of these could be the area of Circle ?
A. About 100 inches squared
B. About 300 inches squared
C. About 900 inches squared
D. About 2700 inches squared

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Circle has a diameter of approximately 20 inches and an area of approximately 300 inches squared. Which of these could be the area of Circle ? A. About 100 inches squared B. About 300 inches squared C. About 900 inches squared D. About 2700 inches squared