Final answer:
To find the required clay amount for a model 3 times the corresponding lengths, calculate the cube of the scaling factor multiplied by the original volume. The result for the new model is 810 cm^3.
Step-by-step explanation:
The question involves applying principles of scaling and proportionality to determine the amount of modeling clay needed for a scaled-up version of a model. When a model is scaled up, the volume increases by the cube of the scaling factor. In this case, the scaling factor is 3, since the corresponding lengths of the new model are 3 times those of the original.
First, find the volume of the original model, which we know is 30 cm3. To find the volume of the new model, we calculate:
Volumenew = (Scale factor)3 × Volumeoriginal
Volumenew = 33 × 30 cm3
Volumenew = 27 × 30 cm3
Volumenew = 810 cm3
Therefore, 810 cm3 of clay would be needed to create a model that is 3 times the corresponding lengths of the original model.