In a circle, a \( 180^{\circ} \) sector has area \( 98 \pi \mathrm{in}^{2} \). What is the radius of the circle? The radius of the circle is \( \square \mathrm{in} \). (Simplify your answer.)

```markdown **Step 1: Recognize the Relationship** - A \(180^\circ\) sector represents half of a full circle. - The area of the entire circle is given by \( \pi r^2 \). - Therefore, the area of a \(180^\circ\) sector is: \[ \frac{1}{2} \pi r^2 \] **Step 2: Set Up the Equation** - We are told that the area of the \(180^\circ\) sector is \( 98\pi \) in\(^2\). - This gives us the equation: \[ \frac{1}{2} \pi r^2 = 98\pi \] **Step 3: Solve for \( r \)** - Multiply both sides of the equation by \(2\) to eliminate the fraction: \[ \pi r^2 = 196\pi \] - Divide both sides by \(\pi\): \[ r^2 = 196 \] - Take the square root of both sides: \[ r = \sqrt{196} = 14 \] **Final Answer:** The radius of the circle is \( \boxed{14 \text{ in}} \). ```