Final answer:
To find the diameter of a larger sphere with a volume 64 times that of a smaller sphere with a 2 cm diameter, we use the sphere volume formula, revealing that the larger sphere has a diameter of 8 cm.
Step-by-step explanation:
The subject of this question is Mathematics, specifically regarding the calculation of volume of a sphere and its relation to the sphere's diameter. The question comes from a High School curriculum.
To find the diameter of the larger sphere, when the volume of one is 64 times larger than the volume of the smaller, we must consider the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume and r is the radius. Since the diameter of the smaller sphere is given as 2 cm, its radius is 1 cm.
The volumes of two spheres are related by the cube of the ratio of their radii. As the volume of the larger sphere is 64 times the volume of the smaller one, the ratio of their radii will be the cube root of 64, which is 4.
Therefore, the radius of the larger sphere is 4 times the radius of the smaller sphere, making it 4 cm, which results in a diameter of 8 cm for the larger sphere.