Question

2.3.3 quiz: circles centered at the origin question 3 of 10 the equation for the circle below is x² + y² = 16. what is the length of the circles radius? a. 32 b. 16 c. 8

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle centered at the origin is $x^{2}+y^{2}=r^{2}$, where $r$ is the radius of the circle.

Step2: Compare with given equation

Given the equation $x^{2}+y^{2}=16$, and comparing it with $x^{2}+y^{2}=r^{2}$, we can see that $r^{2}=16$.

Step3: Solve for the radius

Taking the square - root of both sides of the equation $r^{2}=16$, we get $r = 4$ (we consider the positive value since the radius is a non - negative quantity). To find the circumference $C$ of a circle, the formula is $C = 2\pi r$. Substituting $r = 4$ into the formula, we have $C=2\pi\times4 = 8\pi$. But if we assume the question is asking for the length of the diameter $d$ (since the problem statement seems a bit unclear about what "length" means, and diameter is a common length - related property of a circle), and we know that $d = 2r$. Since $r = 4$, $d=8$.

Answer:

C. 8