The area of a circle is $$ 16 \pi $$ in $$ ^{2} $$. What is the circumference, in inches? Express your answer in terms of $$ \pi $$.

Question

UpStudy AI · Accepted Answer

1. The area of a circle is given by the formula:
   $$
   A = \pi r^2
   $$

2. We are given that $$ A = 16\pi $$. Substitute this into the formula:
   $$
   16\pi = \pi r^2
   $$

3. Divide both sides by $$\pi$$ to solve for $$ r^2 $$:
   $$
   16 = r^2
   $$

4. Taking the square root of both sides, we find the radius:
   $$
   r = 4
   $$

5. The circumference of a circle is given by:
   $$
   C = 2\pi r
   $$

6. Substitute $$ r = 4 $$ into the circumference formula:
   $$
   C = 2\pi (4) = 8\pi
   $$

Thus, the circumference of the circle is $$ 8\pi $$ inches.
The circumference is $$ 8\pi $$ inches.

The area of a circle is \( 16 \pi \) in \( ^{2} \). What is the circumference, in inches? Express your answer in terms of \( \pi \).