## Answer :

### Step-by-Step Solution:

1.

**Identify the given information and relevant formulas:**

- Given the circumference (C) of the circle: [tex]\( C = 16 \)[/tex] inches

- The formula for the circumference of a circle is:

[tex]\[ C = 2 \pi r \][/tex]

- The formula for the area of a circle is:

[tex]\[ A = \pi r^2 \][/tex]

2.

**Solve for the radius [tex]\( r \)[/tex]:**

- Use the circumference formula to solve for the radius [tex]\( r \)[/tex]:

[tex]\[ 16 = 2 \pi r \][/tex]

- Divide both sides of the equation by [tex]\( 2 \pi \)[/tex]:

[tex]\[ r = \frac{16}{2 \pi} \][/tex]

- Simplify the division:

[tex]\[ r = \frac{8}{\pi} \][/tex]

3.

**Calculate the area [tex]\( A \)[/tex]:**

- Use the radius [tex]\( r \)[/tex] in the area formula:

[tex]\[ A = \pi r^2 \][/tex]

- Substitute [tex]\( r = \frac{8}{\pi} \)[/tex] into the area formula:

[tex]\[ A = \pi \left( \frac{8}{\pi} \right)^2 \][/tex]

- Simplify the expression inside the parentheses:

[tex]\[ \left( \frac{8}{\pi} \right)^2 = \frac{64}{\pi^2} \][/tex]

- Multiply this by [tex]\( \pi \)[/tex]:

[tex]\[ A = \pi \cdot \frac{64}{\pi^2} \][/tex]

- Simplify the multiplication (the [tex]\( \pi \)[/tex] in the numerator and one [tex]\( \pi \)[/tex] in the denominator cancel out):

[tex]\[ A = \frac{64}{\pi} \][/tex]

### Final Answer:

The area of the circle, in square inches, expressed in terms of [tex]\(\pi\)[/tex], is:

[tex]\[ A = \frac{64}{\pi} \, \text{in}^2 \][/tex]

Submit this answer as [tex]\(\frac{64}{\pi} \, \text{in}^2\)[/tex].