Geometry

Question Analysis
This question focuses on the similarity of spheres and using the ratio of their radii to find the volume of the larger sphere.
The main point is applying the fact that for similar spheres, the ratio of volumes is the cube of the ratio of their radii.

Key Concept Explanation
The volume formula for a sphere is .
For two similar spheres with radii and , the ratio of their volumes .
This is because the volume of a sphere depends on the cube of its radius, and similar spheres scale proportionally in all directions.

Step-by-Step Solution
Let the radius of the small sphere cm and the radius of the large sphere cm, with the volume of the small sphere cubic cm and the volume of the large sphere

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