To determine the correct statement about the circle with a diameter of 4 inches, let's go through the detailed, step-by-step solution for finding both the circumference and area of the circle.
### Given:
- Diameter of the circle = 4 inches
### Step-by-step Solution:
1. Find the radius of the circle:
- Radius (r) = Diameter / 2
- Radius = 4 inches / 2
- Radius = 2 inches
2. Calculate the circumference of the circle:
- The formula for the circumference (C) is: [tex]\( C = 2 \times \pi \times r \)[/tex]
- Using the radius we found:
- [tex]\( C = 2 \times \pi \times 2 \)[/tex]
- [tex]\( C = 4 \times \pi \)[/tex]
- Using [tex]\(\pi \approx 3.14159\)[/tex]:
- [tex]\( C \approx 4 \times 3.14159 \)[/tex]
- [tex]\( C \approx 12.566370614359172 \)[/tex] inches
3. Calculate the area of the circle:
- The formula for the area (A) is: [tex]\( A = \pi \times r^2 \)[/tex]
- Using the radius we found:
- [tex]\( A = \pi \times 2^2 \)[/tex]
- [tex]\( A = \pi \times 4 \)[/tex]
- Using [tex]\(\pi \approx 3.14159\)[/tex]:
- [tex]\( A \approx 3.14159 \times 4 \)[/tex]
- [tex]\( A \approx 12.566370614359172 \)[/tex] square inches
### Comparison of Numerical Values:
- The numerical value of the circumference is approximately 12.566370614359172 inches.
- The numerical value of the area is approximately 12.566370614359172 square inches.
### Conclusion:
- The statement "The numerical values of the circumference and area are equal" is true because both the circumference and the area are approximately 12.566370614359172.
So, the correct statement is:
- "The numerical values of the circumference and area are equal."
