CBSE · Class 9 · Mathematics · Surface Areas and VolumesIf the radius of a sphere is doubled, its volume becomes how many times of the original volume?
Step-by-Step Solution
The volume of a sphere is $V = \frac{4}{3}\pi r^3$. If the radius $r$ is doubled ($r' = 2r$), the new volume is $V' = \frac{4}{3}\pi (2r)^3 = \frac{4}{3}\pi (8r^3) = 8 \times \left(\frac{4}{3}\pi r^3\right) = 8V$. Thus, the volume becomes 8 times. Therefore, the correct option is 8 times.
Detailed Options Breakdown
Option : 2 times
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
Option 1: 4 times
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
Option 2: 8 times (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: 16 times
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Surface Areas and Volumes.
💡 Study Guide: This question tests core syllabus concepts from Surface Areas and Volumes. For formulas, key summaries, and mock exam reference guides, read the full Surface Areas and Volumes Revision Notes.