Final answer:
One cubic decimeter is equivalent to 1,000 cubic centimeters, because the conversion factor for length units (1 dm to 10 cm) is cubed when converting to units of volume.
Step-by-step explanation:
To determine the equivalent of a cubic decimeter (dm³) in cubic centimeters (cm³), one must understand the relationship between these two units of volume.
One cubic decimeter (dm³) is equal to 1000 cubic centimeters (cm³). This means that there are 1000 cm³ in 1 dm³.
A cubic decimeter is a cube with dimensions of 1 dm on each side. Since 1 decimeter equals 10 centimeters, when converting to cubic centimeters, we have to cube the conversion factor:
1 dm × 1 dm × 1 dm = (10 cm × 10 cm × 10 cm) = 1,000 cm³.
Therefore, 1 cubic decimeter is equal to 1,000 cubic centimeters.
The correct answer to the student's question is therefore:
cubic decimeter = 1,000 cubic centimeters.