ladratic HW Score: $72.22 \%, 13$ of 18 points Points: 0 of 1 A can of beans has surface area $349 \mathrm{~cm}^{2}$. Its height is $19 \mathrm{~cm}$. What is the radius of the circular top?

Step 1 ：We are given that a can of beans has a surface area of \(349 \mathrm{~cm}^{2}\) and its height is \(19 \mathrm{~cm}\). We are asked to find the radius of the circular top.

Step 2 ：We know that the surface area of a cylinder is given by the formula \(2\pi r(r+h)\), where \(r\) is the radius and \(h\) is the height.

Step 3 ：Substituting the given values into the formula, we get \(349 = 2\pi r(r+19)\).

Step 4 ：Solving this equation for \(r\), we find that the radius is approximately \(6.045\) cm.

Step 5 ：Final Answer: The radius of the circular top is \(\boxed{6.045}\) cm.