Calculus project complete: Lidless box

thingiverse

It appears you've posted a response from a math teacher or educator who has guided students through a hands-on activity involving calculating the volume of an object using calculus. The problem they solved is finding the maximum volume of a box with dimensions based on the relationship between the height, width, and length (X). They used derivatives to find critical points, factored the quadratic equation, completed the square, and finally found two solutions for X. Here's how you might respond to the teacher: Your students are right on track. Using derivatives to solve real-world problems is an exciting application of calculus. By completing the square and solving for the critical point, they've identified where the volume function has its maximum value. Their results make sense, given the original dimensions of the box (X=12). The final calculation of 32835.28 is indeed close to the expected result. I'm glad your students are enjoying this hands-on approach to learning calculus. It's great that they can relate their mathematical concepts to real-world problems and even see tangible results. This type of experiential learning can be very engaging and effective in teaching complex math concepts. Keep up the good work, and I'm sure your students will continue to appreciate the power and applicability of derivatives!