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:

When given a modified radius, always substitute it into the standard formula before simplifying. Here, \( R = 2r \) was used in \( V = \frac{4}{3} \pi R^3 \).

Answer 1

The Correct Option is A

Step 1: Identify the formula The volume of a sphere is given by: \[ V = \frac{4}{3} \pi R^3 \] where \( R \) is the radius of the sphere. Given that \( 2r \) is the radius: \[ R = 2r \] Step 2: Substitute \( R = 2r \) into the formula \[ V = \frac{4}{3} \pi (2r)^3 \] \[ = \frac{4}{3} \pi (8r^3) \] \[ = \frac{32\pi r^3}{3} \] Step 3: Conclusion Thus, the correct answer is: \[ \frac{32\pi r^3}{3} \]