1. **Problem:** Graph the circle given by the equation $x^2 + y^2 = 27$ and find its radius. 2. **Formula:** The general equation of a circle centered at the origin is $x^2 + y^2 = r^2$, where $r$ is the radius. 3. **Step:** Compare $x^2 + y^2 = 27$ with $x^2 + y^2 = r^2$ to find $r$. 4. **Calculation:** $r = \sqrt{27} = 3\sqrt{3}$. 5. **Explanation:** The radius is the square root of the constant on the right side of the equation. --- 1. **Problem:** Graph the circle $x^2 + y^2 = 16$ and find its radius. 2. **Step:** $r = \sqrt{16} = 4$. --- 1. **Problem:** Graph the circle $x^2 + y^2 = 32$ and find its radius. 2. **Step:** $r = \sqrt{32} = 4\sqrt{2}$. --- 1. **Problem:** Graph the circle $x^2 + y^2 - 18 = 0$ and find its radius. 2. **Step:** Rewrite as $x^2 + y^2 = 18$. 3. **Step:** $r = \sqrt{18} = 3\sqrt{2}$. --- 1. **Problem:** Graph the circle $x^2 + y^2 - 45 = 0$ and find its radius. 2. **Step:** Rewrite as $x^2 + y^2 = 45$. 3. **Step:** $r = \sqrt{45} = 3\sqrt{5}$. --- **Summary:** Each equation represents a circle centered at the origin with radius $r = \sqrt{\text{constant}}$.