Building off of what they did for this activity, students then found the surface area of objects by measuring their sides and finding the areas of each face. They started with rectangular prisms and then moved on to other types, including a triangular prism, trapezoidal prism, and even a hexagonal prism. Students worked cooperatively in groups to find the dimensions of these shapes and determine their total surface areas.
Next, students started to look at cylinders. Using what they already knew about surface area, students knew that they needed to find the area of each surface to find the total surface area. Students were given two cans and told to determine how much wrapping paper it would take to cover each of them. Working with their groups, students quickly determined that they needed to use the formula for the area of a circle to cover the top and bottom of the can. Given the hint that they would need to unwrap the label of the can, students discovered that the label was a rectangle when unwrapped and were able to find its area. As they continued to discuss the problem with their group members, students soon determined that the length of the label was the same as the circumference of the circles. Putting together everything they had done, students were able to develop the general formula for finding the surface area of a cylinder.
Here are some pictures of the students working together with their groups to find the surface area of cans: