Maximizing Lantern Volume From A Rectangle

A rectangle with fixed perimeter 72 cm is folded into 6 equal strips that become the lateral faces of a hexagonal paper lantern. The animation shows how the strip width and height relate through the perimeter constraint, then builds the volume as a function of one variable. Using calculus to find the critical point reveals the dimensions that produce the maximum possible lantern volume, useful for students studying optimization problems.

Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy

The prompt that made it

Từ một hình chữ nhật có chu vi 72 cm, gấp nó thành 6 mặt bằng nhau rồi gập lại thành các mặt bên của lồng đèn. Khi đó thể tích lớn nhất của lồng đèn là bao nhiêu? Audience: High school student

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Make the next one in this series

• Show how volume changes as the hexagon side length varies using a live graph
• Compare the maximum volume of a hexagonal lantern to a square-based lantern with the same perimeter
• Derive the general formula for maximum volume of an n-sided prism lantern from a fixed perimeter