Student will discover the relationship between the height of a box with a triangular base and its volume and student will find the height that will produce the maximum volume of the open-topped box.
Before the Activity
This activity should follow the Open-box activity.
Give each student two copies of the Triangle Box Template and have them produce an open-topped box with a triangular base. Students should measure the height and determine the area of the base, using the 30-60-90 triangle relationships. Then students should determine the volume of the box.
During the Activity
Each student needs the file TriangleBox.tns on their handhelds to carry out the activity.
After the Activity
In this extension, student will explore another property of the dimensions of the box when its size is at maximum volume.
Before students can begin this activity, they need to have worked through the Box Problem and the Triangle Box Problem. It may also be necessary for students to build the open-topped triangular box to help them visualize the box.
Students should discover that when a box with a triangular base is built so that it has maximum volume, that the total area of the walls of the box is equal to the area of the base.