Pyramid Volume Challenge

Links to Activity

Main Concepts

Multivariable Calculus

Partial Derivatives

Tangent Planes


25 minutes in class

Summary of Activity

Students are given the challenge to find the volume of a pyramid defined as tangent to a certain surface and bounded by the three standard planes, with respect to the coordinates of the point of tangency

Notes and Insights

This problem allows for at least two different solutions depending on how the function F is set up.

A possible extension is to ask the students to set up a similar problem in the two dimensional plane.

Another extension is to consider the problem in reverse. We fix the volume of a tetrahedron and think about the space that the tetrahedron can cover in the first octant if it moves around. That is the notion of envelope, and it requires a lot more tools than what we have in this course.