Question

A cylindrical can of vegetables has a label wrapped around the outside, touching end to end. The only parts of the can not covered by the label are the circular top and bottom of the can. If the area of the label is 66π square inches and the radius of the can is 3 inches, what is the height of the can?

Answer 1

We can begin by finding the total surface area of the can. The area of the label is given as 66π square inches. Since the label is wrapped around the outside of the can, the area covered by it is the lateral surface area of the cylinder. The lateral surface area of a cylinder is given by 2πrh, where r is the radius and h is the height of the cylinder. We can write the equation for the lateral surface area as: 2πrh = 66π Simplifying this equation, we get: rh = 33 We also know that the radius of the can is given as 3 inches. Substituting this value in the above equation, we get: 3h = 33 Solving for h, we get: h = 11 inches Therefore, the height of the can is 11 inches.