To find the radius of a circle given the equation [tex]\( x^2 + y^2 = 16 \)[/tex], we need to recognize the standard form of a circle's equation, which is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
where [tex]\( r \)[/tex] represents the radius of the circle, and [tex]\( r^2 \)[/tex] is the radius squared.
In the given equation [tex]\( x^2 + y^2 = 16 \)[/tex], it is evident that the term on the right side of the equation, 16, represents [tex]\( r^2 \)[/tex].
Thus, we must find the value of [tex]\( r \)[/tex] by taking the square root of both sides of the equation [tex]\( r^2 = 16 \)[/tex]:
[tex]\[ r = \sqrt{16} \][/tex]
The square root of 16 is 4. Therefore, the radius [tex]\( r \)[/tex] of the circle is:
[tex]\[ r = 4 \][/tex]
Hence, the radius of the circle is 4.
The correct answer is:
A. 4
