Log inSign up
AP Calculus AB · Question of the Day

AP Calculus AB Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.
Thursday, November 5, 2026

A box with square base and no lid has volume 32 ft332\text{ ft}^3. To minimize cost, what should be minimized?

Keep practicing AP Calculus AB

Question of the Day

Answer today's AP Calculus AB question, reveal the full explanation, then keep the streak going with a new question every day.

A box with square base and no lid has volume 32 ft332\text{ ft}^3. To minimize cost, what should be minimized?

  1. The volume of the box
  2. The total surface area of cardboard used (base plus four sides) (correct answer)
  3. The base area only
  4. The height only
  5. The perimeter of the square base

Explanation: This question tests the skill of setting up optimization problems by identifying the quantity to be minimized for a box with fixed volume. The box has a square base and no lid, with a volume of 32 ft³, and to minimize cost, we minimize the total surface area of the cardboard used, which includes the base and four sides. The cost is assumed proportional to the surface area, so we relate the side length of the base and height through the volume constraint. Expressing the surface area as a function of one variable allows us to find the dimensions that use the least material. A tempting distractor is choice A, the volume of the box, but this is fixed at 32 ft³ and not what we minimize. In optimization problems for open containers with fixed volume, always model the surface area as the objective function using the volume constraint to minimize material costs.