Question

If the radius of a sphere becomes \(3\) times, then its volume will become:

• A. \(3\) times
• B. \(6\) times
• C. \(9\) times
• D. \(27\) times

Hint:

For similar 3D shapes, volumes scale with the cube of the linear scale factor: if \(r\to kr\), then \(V\to k^{3}V\).

Answer 1

The Correct Option is D

Step 1: Recall the volume formula of a sphere.
\(V=\dfrac{4}{3}\pi r^{3}\). Thus, volume is proportional to \(r^{3}\).
Step 2: Apply the scaling.
If \(r\) becomes \(3r\), then the new volume \(V'\propto (3r)^{3}=27r^{3}\).
Step 3: Conclude.
Hence, the volume becomes \(27\) times the original.