B17. [Hard – WP] (Replaces Q42) A rectangular box has a square base and a total…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

B17. [Hard – WP] (Replaces Q42) A rectangular box has a square base and a total surface area of exactly 216 cm2216\text{ cm}^2. What is the maximum possible volume of the box? Hint: Express the height in terms of the base side length, then write volume as a single-variable function and find its maximum.

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