A sphere has a radius of 17 5 feet. What is the volume, in cubic feet,

Choice D is correct. The volume, $V$, of a sphere can be found using the formula $V=\frac{4}{3}\pi r^3$, where $r$ is the radius of the sphere. It’s given that the sphere has a radius of $\frac{17}{5}$ feet. Substituting $\frac{17}{5}$ for $r$ in the formula $V=\frac{4}{3}\pi r^3$ yields $V=\frac{4}{3}\pi {\left(\frac{17}{5}\right)}^3$, which is equivalent to $V=\frac{4}{3}\pi \left(\frac{\mathrm{4,913}}{125}\right)$, or $V=\frac{\mathrm{19,652}\pi }{375}$. Therefore, the volume, in cubic feet, of the sphere is $\frac{\mathrm{19,652}\pi }{375}$.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the volume, in cubic feet, of a sphere with a radius of $\sqrt[3]{\frac{17}{5}}$ feet.

Choice C is incorrect and may result from conceptual or calculation errors.