Homework
Question 6, 1.5.33
A can of beans has surface area $319 \mathrm{~cm}^{2}$. Its height is $19 \mathrm{~cm}$. What is the radius of the circular top?
Answer
Final Answer: The radius of the circular top is \(\boxed{5.5}\) cm.
Step 1 ：We are given that a can of beans has a surface area of \(319 \mathrm{~cm}^{2}\) 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 \(319 = 2\pi r(r+19)\).
Step 4 ：Solving this equation for \(r\), we find that the radius is approximately \(5.5\) cm.
Step 5 ：Final Answer: The radius of the circular top is \(\boxed{5.5}\) cm.
