5. Information about three circles is listed below. . Circle $$ P $$ has a radius of 26 cm . . Circle $$ Q $$ has a diameter of 52 cm . Based on the informatius of 52 cm . A The area of Circle $$ Q $$ is larger than the area of Circle $$ R $$. B The area of Circle $$ P $$ is the smallest of all three circles. C The circumference of Circle $$ Q $$ is the same as Circle $$ R $$. D The circumference of Circle $$ Q $$ is the same as Circle $$ P $$.

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UpStudy AI · Accepted Answer

It appears you're presenting a multiple-choice question involving three circles: $$ P $$, $$ Q $$, and $$ R $$. However, information about Circle $$ R $$ is missing from your description. To provide an accurate analysis, I'll focus on the details provided for Circles $$ P $$ and $$ Q $$.

### Given Information:
1. **Circle $$ P $$**
   - **Radius**: 26 cm

2. **Circle $$ Q $$**
   - **Diameter**: 52 cm
   - **Radius**: Since the diameter is 52 cm, the radius of Circle $$ Q $$ is $$ \frac{52}{2} = 26 $$ cm

### Analysis of the Statements:
Let's evaluate each statement based on the provided information.

**A. The area of Circle $$ Q $$ is larger than the area of Circle $$ R $$.**

- **Cannot Determine**: Without information about Circle $$ R $$, we cannot compare the areas.

**B. The area of Circle $$ P $$ is the smallest of all three circles.**

- **Cannot Determine**: Since Circle $$ Q $$ has the same radius as Circle $$ P $$, their areas are identical. Without information about Circle $$ R $$, we can't conclude whether Circle $$ P $$'s area is the smallest.

**C. The circumference of Circle $$ Q $$ is the same as Circle $$ R $$.**

- **Cannot Determine**: Without information about Circle $$ R $$, this statement cannot be evaluated.

**D. The circumference of Circle $$ Q $$ is the same as Circle $$ P $$.**

- **True**: Both Circle $$ P $$ and Circle $$ Q $$ have the same radius (26 cm). The circumference $$ C $$ of a circle is given by:
  $$
  C = 2\pi r
  $$
  Since both circles have $$ r = 26 $$ cm:
  $$
  C_P = C_Q = 2\pi \times 26 \text{ cm} = 52\pi \text{ cm}
  $$
  Therefore, their circumferences are identical.

### Conclusion:
Based on the provided information, **Statement D** is **correct**.

**Answer:**  
D. The circumference of Circle $$ Q $$ is the same as Circle $$ P $$.
The circumference of Circle $$ Q $$ is the same as Circle $$ P $$.

Upstudy AI Solution

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Given Information:

Analysis of the Statements:

Conclusion:

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