Question

Sanna is packing small boxes inside a larger box. The base of the large box is 50 by 75cm and it is 30cm high. The small boxes are 5cm by 4cm by 2cm and weigh 10g each. How many small boxes will fit in the large one?

Answer 1

2808

Explanation:

Sanna can pack 12 layers of 225 small boxes by aligning the 5 cm dimension with the 75 cm dimension (15 boxes) and the 2 cm dimension with the 30 cm dimension (15 boxes).

That will leave an empty space 2 cm by 75 cm by 30 cm. In that space, Sanna can pack an additional 108 boxes by aligning the 4 cm dimension with the 75 cm dimension (18 boxes) and the 5 cm dimension with the 30 cm dimension (6 boxes).

Altogether, Sanna has packed 12 layers of 225 boxes each and 1 layer of 108 boxes, for a total of ...

12×225 + 108 = 2700 +108 = 2808 . . . small boxes

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The empty space will have a dimension of 2 cm by 3 cm by 30 cm.