Question

If the diameter of a sphere is d, then its volume is

• A. \(\frac{1}{6} \pi d^3\)
• B. \(\frac{4}{3} \pi d^3\)
• C. \(\frac{1}{24} \pi d^3\)
• D. \(\frac{1}{3} \pi d^3\)

Answer 1

The Correct Option is A

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 \(\frac{1}{6} \pi d^3\).