To determine the radius of the circle given the equation [tex]\( x^2 + y^2 = 16 \)[/tex], let's examine the equation and compare it to the standard form of a circle equation.
The standard form of the equation of a circle centered at the origin (0, 0) is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
In the given problem, the equation of the circle is:
[tex]\[ x^2 + y^2 = 16 \][/tex]
We can see that this matches the standard form [tex]\( x^2 + y^2 = r^2 \)[/tex], where [tex]\( r^2 = 16 \)[/tex].
To find the radius [tex]\( r \)[/tex], we need to take the square root of both sides of the equation:
[tex]\[ r^2 = 16 \][/tex]
[tex]\[ r = \sqrt{16} \][/tex]
[tex]\[ r = 4 \][/tex]
Therefore, the radius of the circle is [tex]\( 4 \)[/tex]. So, the correct answer is:
D. 4
