Circle P has a radius of 7, and Circle R has a diameter of 8. The circumference of Circle P is how much greater than the circumference of Circle R?

Options

A. `pi`
B. `6pi`
C. `16pi`
D. `33pi`

Answer

To solve the problem, we need to find the circumferences of Circle P and Circle R, and then determine how much greater the circumference of Circle P is compared to Circle R.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The radius of Circle P (RP) is given as 7.
- The diameter of Circle R (DR) is given as 8.

2. **Calculate the Radius of Circle R:**
- The radius of Circle R (RR) can be calculated using the formula:
\[ RR = \frac{DR}{2} = \frac{8}{2} = 4 \]

3. **Calculate the Circumference of Circle P:**
- The formula for the circumference (C) of a circle is:
\[ C = 2 \pi R \]
- For Circle P:
\[ CP = 2 \pi RP = 2 \pi (7) = 14 \pi \]

4. **Calculate the Circumference of Circle R:**
- For Circle R:
\[ CR = 2 \pi RR = 2 \pi (4) = 8 \pi \]

5. **Find the Difference in Circumference:**
- To find out how much greater the circumference of Circle P is than Circle R, we subtract the circumference of Circle R from that of Circle P:
\[ CP - CR = 14 \pi - 8 \pi = 6 \pi \]

6. **Conclusion:**
- The circumference of Circle P is \(6 \pi\) greater than the circumference of Circle R.

### Final Answer:
The circumference of Circle P is \(6 \pi\) greater than the circumference of Circle R.

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