Answer
The area of Circle \( B \) could be about 300 or 900 square inches. The best answer is C. About 900 inches squared.
Solution
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**.
Reviewed and approved by the UpStudy tutoring team
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