Find the circumference and the area of a circle with a radius of 3 in.

To find the circumference and the area of a circle, we use the formulas:

- **Circumference** \((C)\): \( C = 2\pi r \)
- **Area** \((A)\): \( A = \pi r^2 \)

Where \( r \) is the radius of the circle.

Given that the radius \( r = 3 \) inches, we can substitute this value into the formulas:

1. **Circumference**:
   \[
   C = 2\pi \times 3 = 6\pi \text{ inches}
   \]
   Approximating \(\pi\) as 3.14159, we get:
   \[
   C \approx 6 \times 3.14159 \approx 18.84954 \text{ inches}
   \]

2. **Area**:
   \[
   A = \pi \times 3^2 = \pi \times 9 = 9\pi \text{ square inches}
   \]
   Approximating \(\pi\) as 3.14159, we get:
   \[
   A \approx 9 \times 3.14159 \approx 28.27431 \text{ square inches}
   \]

Thus, the circumference of the circle is approximately 18.85 inches, and the area is approximately 28.27 square inches.

Would you like more details or have any questions? Here are some related questions:

1. How do you derive the formula for the circumference of a circle?
2. What is the relationship between the diameter and the circumference of a circle?
3. How do you derive the formula for the area of a circle?
4. What are the applications of circle circumference and area calculations in real life?
5. How do the formulas for circumference and area change if using a diameter instead of a radius?
6. What is the difference between calculating the perimeter and the circumference?
7. Can you calculate the area and circumference using only the diameter?
8. What are some historical methods of approximating \(\pi\)?

**Tip**: Remember that \(\pi\) is an irrational number, so for precise calculations, use more decimal places or a \(\pi\) button on your calculator.

Learn how to find the circumference and area of a circle with a radius of 3 inches using mathematical formulas. Step-by-step solution with approximations provided. Suitable for Grades 6-8.

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