Knapsack problem on 2D or 3D space

Question

Considering a series of rectangle items with known size $(a_1,b_1),(a_2,b_2)\cdots,(a_n,b_n)$, and a big rectangle box with size $(A,B)$

Question 1: How to fill the box with the items that minimize the blank area?

Question 2: Aiming at "take all the items away" with multiple boxes, how to minimize the number of the boxes? (Can I just employ the algorithm in Question 1 repeatly to solve it?)

Question 3: How about cuboid items and box?

Sincerely thank you for your reading.

Answer 1

1. Can the rectangles be rotated? If so, by an arbitrary angle or only 90 degrees?
2. This is a 2D bin packing problem. Your proposed greedy algorithm is reasonable but not guaranteed to yield an optimal solution.
3. 3D bin packing problem