Answer
See below
Work Step by Step
Let $x$ be the length of the cube's edge.
The volume of the sphere: $V_{sphere}\\=\frac{4}{3}\pi r^3\\=\frac{4}{3}\pi(\frac{x}{2})^3\\=\frac{1}{6}\pi x^3$
The surface area of the sphere: $SA_{sphere}\\=4\pi r^2\\=4\pi (\frac{x}{2})^2\\=\pi x^2$
The volume of the cube: $V_{cube}\\=x^3$
The surface area of the cube: $SA_{cube}\\=6x^2$
The ratio for the sphere: $\frac{SA_{sphere}}{V_{sphere}}=\frac{\pi x^2}{\frac{1}{6}\pi x^3}=6x^{-1}$
The ratio for the cube: $\frac{SA_{cube}}{V_{cube}}=\frac{6x^2}{x^3}=x^{-1}$
Hence, the ratios of both geometries are the same.
