To determine the radius of the circle given the equation [tex]\(x^2 + y^2 = 64\)[/tex], we will compare it with the standard form of a circle's equation.
1. Understand the Standard Form: The standard form of the equation for a circle centered at the origin ([tex]\(0, 0\)[/tex]) is [tex]\(x^2 + y^2 = r^2\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle.
2. Identify [tex]\(r^2\)[/tex]: From the given equation [tex]\(x^2 + y^2 = 64\)[/tex], we see that [tex]\(r^2 = 64\)[/tex].
3. Solve for [tex]\(r\)[/tex]: To find the radius ([tex]\(r\)[/tex]):
[tex]\[
r = \sqrt{64}
\][/tex]
4. Calculate the Numerical Value:
[tex]\[
\sqrt{64} = 8
\][/tex]
Therefore, the radius of the circle is [tex]\(8\)[/tex].
The correct answer is:
C. 8
