Question

If \( 2r \) is the radius of a sphere, then its volume is:

• A. \( \frac{32\pi r^3}{3} \)
• B. \( \frac{16\pi r^3}{3} \)
• C. \( \frac{8\pi r^3}{3} \)
• D. \( \frac{64\pi r^3}{3} \)

Hint:

For a sphere, the volume formula is: \[ V = \frac{4}{3} \pi R^3 \]

Answer 1

The Correct Option is A

The volume of a sphere is given by:
\[ V = \frac{4}{3} \pi R^3 \] Since \( 2r \) is the radius, we substitute \( R = 2r \):
\[ V = \frac{4}{3} \pi (2r)^3 \] \[ = \frac{4}{3} \pi (8r^3) = \frac{32\pi r^3}{3} \]