To find the radius of a sphere given its surface area, we can use the formula for the surface area of a sphere:
\[ A = 4\pi r^2 \]
where \(A\) is the surface area and \(r\) is the radius.
Given that the surface area \(A = 184.96 , \text{cm}^2\), we can set up the equation:
\[ 184.96 = 4\pi r^2 \]
To isolate \(r^2\), we can divide both sides by \(4\pi\):
\[ r^2 = \frac{184.96}{4\pi} \]
Next, we can calculate \(4\pi\):
\[ 4\pi \approx 12.5664 \]
Now, substituting this value into the equation:
\[ r^2 = \frac{184.96}{12.5664} \approx 14.71 \]
To find \(r\), we take the square root of \(r^2\):
\[ r = \sqrt{14.71} \approx 3.84 , \text{cm} \]
Thus, the radius of the sphere is approximately \(3.84 , \text{cm}\).