The net for a conical paper cup is formed by cutting a sector from a circular piece of paper. What sector angle creates a net that maximizes the cone's volume? In this activity students will build concrete models, measure the dimensions and calculate the volume. Next, students will use a construction to gather data, make a scatter plot and determine the sector angle that maximizes the volume.
Before the Activity
Teachers should review the activity and solution prior to using it in class.
Students create paper nets for various cones using an included BLM. Students measure dimensions and calculate volumes of the cones.
During the Activity
Students complete the activity in pairs.
After the Activity
Lead a discussion to consolidate student understanding. Possible extensions are listed in the teacher plan.