How many 3-cm cubes can be packed in a rectangular box measuring 30cm by 20cm by 25cm?

Answer 1

240 cubes.

Each edge of the cube is 3cm long.

Let the box be 30cm long by 20 cm wide by 25 cm high; then:

Along the 30 cm edge, 30 cm ÷ 3 cm = 10 cube edges;

along the 20 cm edge, 20 cm ÷ 3 cm = 6 r 2, so 6 cube edges can fit.

Thus on [the area of] the base of the box, 10 x 6 = 60 cubes can be fitted to form 1 layer.

Up the 25 cm edge, 25 ÷ 3 cm = 8 r 1 cube edges, so 8 layers can be fitted in the box.

But each layer has 60 cubes, giving a total of 8 x 60 = 240 [whole] cubes can be fitted in the box (with some room to spare - 30cm by 2 cm by 1 cm).