To solve the problem of finding the radius of a circle given its area, we can follow these steps:
1. Understand the formula for the area of a circle: The area [tex]\( A \)[/tex] of a circle is given by the formula [tex]\( A = πr^2 \)[/tex], where [tex]\( r \)[/tex] is the radius of the circle.
2. Substitute the given area into the formula: We are given that the area of the circle is [tex]\( 16π \)[/tex] square centimeters. Thus, we have:
[tex]\[
16π = πr^2
\][/tex]
3. Isolate the radius [tex]\( r \)[/tex]: To find the radius, we need to isolate [tex]\( r \)[/tex] on one side of the equation. By dividing both sides of the equation by [tex]\( π \)[/tex], we get:
[tex]\[
16 = r^2
\][/tex]
4. Solve for [tex]\( r \)[/tex]: Take the square root of both sides to solve for the radius:
[tex]\[
r = \sqrt{16}
\][/tex]
5. Calculate the square root: The square root of 16 is 4, so:
[tex]\[
r = 4
\][/tex]
Therefore, the length of the radius of the circle is 4 centimeters.
The correct answer is:
[tex]\[ \boxed{4 \text{ cm}} \][/tex]
