Question

If the diameter of a sphere is \(d\), then its volume will be

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

Hint:

Remember: when diameter \(d\) is given, always convert to radius using \(r = \frac{d}{2}\) before applying sphere formulas.

Answer 1

The Correct Option is D

Step 1: Recall the formula for volume of a sphere.
\[ V = \frac{4}{3} \pi r^3 \]
Step 2: Substitute \(r = \frac{d}{2}\).
\[ V = \frac{4}{3} \pi \left(\frac{d}{2}\right)^3 = \frac{4}{3} \pi \times \frac{d^3}{8} = \frac{\pi d^3}{6} \]
Step 3: Conclusion.
Hence, the volume of the sphere is \(\frac{\pi d^3}{6}\).