Correct answer: \(\frac{1}{6} \pi d^3\)
Explanation:
The formula for the volume of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius of the sphere. The diameter \( d \) is related to the radius by: \[ r = \frac{d}{2} \] Substituting this into the volume formula: \[ V = \frac{4}{3} \pi \left( \frac{d}{2} \right)^3 = \frac{4}{3} \pi \frac{d^3}{8} = \frac{1}{6} \pi d^3 \]
Hence, the volume of the sphere is \(\frac{1}{6} \pi d^3\).