A box with dimensions 15 cm x 25 cm x 30 cm is filled with cubes with dimensions 3 cm x 3 cm x 3 cm. Then 20 cubes were removed from the box. How many cubes are left in the box?

First, let's calculate the volume of the box and the volume of one cube.

Volume of the box: $$V_{box} = 15 \text{ cm} \times 25 \text{ cm} \times 30 \text{ cm} = 11250 \text{ cm}^3$$.

Volume of one cube: $$V_{cube} = 3 \text{ cm} \times 3 \text{ cm} \times 3 \text{ cm} = 27 \text{ cm}^3$$.

Now, let's find out how many cubes can fit into the box. We can do this by dividing the volume of the box by the volume of a cube, but it's more accurate to find how many cubes fit along each dimension:

• Along the 15 cm side: $$15 \text{ cm} \div 3 \text{ cm} = 5$$ cubes.
• Along the 25 cm side: $$25 \text{ cm} \div 3 \text{ cm} = 8$$ cubes (with a remainder, so only 8 whole cubes fit).
• Along the 30 cm side: $$30 \text{ cm} \div 3 \text{ cm} = 10$$ cubes.

The total number of cubes that can fit in the box is $$5 \times 8 \times 10 = 400$$ cubes.

The problem states that 20 cubes were removed from the box. So, the number of cubes remaining in the box is $$400 - 20 = 380$$ cubes.

Answer: 380