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A circle has a diameter of 4 inches. Which statement about the area aroun
OA comparison of the area and circumference of the circle is pot possible bee
to find both.
O The numerical values of the circumference and area are equal.
The numerical value of the circumference is greater than the numerical value of the area
The numerical value of the circumference is less than the
numerical value of the area.

Sagot :

GinnyAnswer
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."
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