Question

A circle has a diameter of 4 inches. Which statement about the area and circumference of the circle is true?
A comparison of the area and circumference of the circle is not possible because there is not enough information to find both.
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.

Answer 1

To analyze the area and circumference of a circle with a diameter of 4 inches, we start with the formulas for both:

1. **Circumference (C)** of a circle is given by:
\[
C = \pi d
\]
where \( d \) is the diameter. Here, \( d = 4 \) inches, so:
\[
C = \pi \times 4 = 4\pi
\]

2. **Area (A)** of a circle is given by:
\[
A = \pi r^2
\]
where \( r \) is the radius. The radius is half of the diameter, so:
\[
r = \frac{d}{2} = \frac{4}{2} = 2 \text{ inches}
\]
Thus, the area is:
\[
A = \pi \times (2)^2 = \pi \times 4 = 4\pi
\]

Now, we compare the numerical values of the circumference and area. We found that:
- Circumference \( C = 4\pi \)
- Area \( A = 4\pi \)

Since both values are equal, the correct statement is:
**The numerical values of the circumference and area are equal.**