Geometry

Question Analysis
This question involves multiple geometric concepts, including the relationship between a sphere inscribed in a cube, the surface area of a cube, and the volume of a sphere.
The main focus is on using the surface area of the cube to find its side length, which is equal to the diameter of the inscribed sphere, and then calculating the volume of the sphere.

Key Concept Explanation
The surface area formula for a cube is , where is the side length of the cube.
For a sphere inscribed in a cube, the diameter of the sphere is equal to the side length of the cube.
The volume formula for a sphere is , with being the radius and .

Step-by-Step Solution
Calculate the side length of the cube: Given square inches, using the formula , we have

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