Final answer:
The volume of a sphere is given by the formula V = (4/3)πr³. To determine the measures, we use the scale factor and the volume of the smaller sphere. The scale factor is x/n and the radius of the larger sphere is the cube root of x/(nπ).
Step-by-step explanation:
The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere. In this question, we are given the volume of the larger sphere as x units. To determine the measures, we need to find the scale factor and the radius of the larger sphere.
Since the volume of a sphere depends on r³, if the scale factor is k, the volume of the larger sphere will be k³ times the volume of the smaller sphere. So, if the volume of the smaller sphere is n units³, the volume of the larger sphere is k³n units³.
Therefore, if the volume of the larger sphere is x units, the scale factor is given by x/n, and the radius of the larger sphere is given by the cube root of x/(nπ).